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THE    LIMITATIONS 


OF  THE 


EXPANSION  OF  STEABI 

FORMING    THE    SIXTEENTH    CHAPTER   OF 

THE  RELATIVE  PROPORTIONS  OP  THE 
STEAM-ENGINE. 


BY 

WILLIAM   DEXXIS   MARKS, 

WHITNEY   PROFESSOR    OF   DYNAMICAL   ENGINEERING    IN   THE    UNUKKSn 
OF    PENNSYLVANIA. 


WITH  NUMEROUS   DIAGRAMS. 


FROM    THIRD    EDITION, 

REVISED    AND    ENLAnCED. 


PHILADELPHIA: 

PRESS   OF   J.  B.  LIPPINCOTT   COMPANY. 

188  7. 


THE    LIMITATIONS 


OF  THE 


EXPANSION  OF  STEAM: 

FORMING   THE    SIXTEENTH    CHAPTER   OP 

THE  RELATIVE  PROPORTIONS  OP  THE 
STEAM-ENGINE. 


BY 

"WILLIAM  DENNIS  MAEKS, 

•WHITNEY  PKOFESSOB  OF  DYNAMICAL   ENGINEERING   IN  THE  UNIVEESITY 
OF   PENNSYLVANIA. 


WITH  NUMEROUS  D I A  G  B^nfJ^:^  ^ 

FROM    THIRD    E  D  I  T  I0N,^^^^9jf?  JTT  |^ 


REVISED   AND   ENLARGED. 


PHILADEIiPHIA: 

PRESS  OF  J.  B.  LIPPINCOTT  C03IPANY. 

1887. 


Copyright,  1887,  by  J.  B.  Lippincott  Company. 


PREFACE. 


The  condensation  of  steam  by  the  walls  of  the  steam- 
cylinder  is  a  fact  whose  existence  has  been  repeatedly  proved 
by  many  distinguished  experimenters. 

Probably  Watt  and  a  long  line  of  followers  knew  that 
great  expansions  meant  greater  proportional  losses  through 
condensation. 

We  take  the  following  paragraphs  regarding  Watt's  work 
from  Galloway's  History  of  the  Steam- Engine ^  page  30 
(Edition  of  1828). 

"  But  in  the  year  1763-64,  having  occasion  to  repair  a 
model  of  Newcomen's  engine  belonging  to  the  Natural  Phi- 
losophy Class  of  the  University,  his  mind  was  again  directed 
to  the  subject.  At  this  period  his  knowledge  was  principally 
derived  from  Desaguliers,  and  partly  from  Belidor.  He  set 
about  repairing  the  model  as  a  mere  mechanician,  and  when 
that  was  done  and  set  to  work,  he  was  surprised  that  its 
boiler  was  not  supplied  with  steam,  though  apparently  quite 
large  enough  (the  cylinder  of  the  model  being  two  inches  in 
diameter  and  six  inches  stroke,  and  the  boiler  about  nine 
inches  in  diameter) ;  by  blowHing  the  fire  it  was  made  to 
take  a  few  strokes,  but  required  an  enormous  quantity  of 
injection  water,  though  it  was  very  lightly  loaded  by  the 
column  of  water  in  the  pump.  It  soon  occurred  to  him  that 
this  was  caused  by  the  little  cylinder  exposing  a  greater  sur- 
face to  condense  the  steam  than  the  cylinders  of  larger  en- 
gines did  in  proportion  to  their  respective  contents,  and  it 
was  found  that  by  shortening  the  column  of  water  the  boiler 


4  PREFACE. 

could  supply  the  cylinder  with  steam  and  the  engine  would 
work  regularly  with  a  moderate  quantity  of  injection.  It 
now  appeared  that  the  cylinders  being  of  brass  would  con- 
duct heat  much  better  than  the  cast-iron  cylinders  of  larger 
engines  (which  were  generally  lined  with  a  strong  crust), 
and  that  considerable  advantage  could  be  gained  by  making 
the  cylinders  of  some  substance  that  would  receive  and  give 
out  heat  the  slowest.  A  small  cylinder  of  six  inches  diam- 
eter and  twelve  inches  stroke  was  constructed  of  wood  pre- 
viously soaked  in  linseed  oil  and  baked  to  dryness.  Some 
experiments  were  made  with  it,  but  it  was  found  that  cylin- 
ders of  wood  were  not  at  all  likely  to  prove  durable,  and  that 
the  steam  which  was  condensed  in  filling  it  still  exceeded  the 
proportion  of  that  which  was  required  in  engines  of  larger 
dimensions.  It  was  also  ascertained  that  unless  the  temper- 
ature of  the  cylinder  itself  were  reduced  as  low  as  that  of  the 
vacuum,  it  would  produce  vapor  of  a  temperature  sufficient 
to  resist  part  of  the  pressure  of  the  atmosphere. 

"All  attempts,  therefore,  to  reduce,  by  a  better  exhaustion 
by  throwing  in  a  greater  quantity  of  injection  water,  was  a 
waste  of  steam,  for  the  larger  quantities  of  injection  cooled 
the  cylinder  so  much  as  to  require  quantities  of  steam  to 
heat  it  again,  out  of  proportion  to  the  power  gained  by 
having  made  a  more  perfect  vacuum." 

Thus  we  see  that  Watt  recognized  the  condensation  due 
to  the  relative  surface  exposed,  as  also  that  due  to  the  dif- 
ference of  temperature  between  exhaust  and  initial  steam. 
With  the  rude  machines  then  in  use,  it  was  out  of  the  ques- 
tion for  him-  to  attempt  to  reduce  the  condensation  by  high 
rotative  speeds. 

In  addition  to  the  experiments  of  Watt,  we  have  a  large 
number  by  D.  K.  Clark,  G.  A.  Hirn,  and  Chief  Engineers 
Isherwood,  Loring,  and  Emery,  all  proving,  under  certain 
conditions,  the  overwhelming  influence  of  initial  condensa- 


PREFACE.  6 

tion  in  the  steam-cylinder ;  but  the  writer  is  not  aware  that 
any  one  of  them  has  established  a  rational  and  general  law 
applicable  in  all  cases  where  the  piston  and  valves  are 
proven  tight. 

In  a  lecture  delivered  at  the  Institute  of  Civil  Engineers, 
May,  1883,  Sir  William  Thomson  used  the  following 
words :  "  In  physical  science,  a  first  essential  step  in  the 
direction  of  learning  any  subject  is  to  find  principles  of 
numerical  reckoning,  and  methods  for  practically  measur- 
ing some  quality  connected  with  it.  I  often  say,  when  you 
can  measure  what  you  are  speaking  about,  and  express  it 
in  numbers,  you  know  something  about  it ;  but  when  you 
cannot  measure  it,  when  you  cannot  express  it  in  numbers, 
your  knowledge  is  of  a  meagre  and  unsatisfactory  kind ;  it 
may  be  the  beginning  of  knowledge,  but  you  have  scarcely 
in  your  thoughts  advanced  to  the  stage  of  science,  whatever 
the  matter  may  be." 

It  was  with  the  feeling  so  well  expressed  by  Professor 
Thomson  that  the  writer  undertook  to  find  out,  as  well  as 
he  could,  whether  the  Newtonian  law  of  cooling  was  appli- 
cable to  the  action  of  steam  inside  the  steam-cylinder. 

So  far  as  he  knows,  no  writer,  from  the  time  of  Carnot  to 
this  present  date,  has  essayed  to  include  all  the  data  which 
must  aflTect  the  condensation  and  expansion  of  steam  in  one 
general  formula  applicable  to  all  cases. 

The  factors  which  must  enter  into  such  a  formula  will  be 
seen  to  be  too  numerous  to  admit  of  the  graphical  treatment 
which,  following  the  high  authority  of  Rankine,  quite  a  num- 
ber of  his  followers  have  essayed,  with  varying  degrees  of 
approximation  to  correctness  of  result,  and  apparently  quite 
oblivious  of  the  fact  that  they  are  reasoning  in  a  circle  from 
empirical  statement  of  experimental  results,  and  that  they 
are  shut  out  completely  from  the  hope  of  logically  searching 
for  the  best  attainable  conditions  in  the  use  of  steam. 


6  PREFACE. 

Should  it  prove  that  this  discussion  of  initial  condensa- 
tion is  a  scaffolding  for  the  walls  and  roof  of  a  structure 
which  will  house  all  the  warring  experimental  proofs  and 
mathematical  discussions  as  to  economy  of  steam,  and  that 
the  hitherto  unknown  law  of  condensation  of  steam  in- 
side of  the  cylinder  of  a  steam-engine  has  been  formulated 
with  practical  accuracy,  the  writer  will  regard  himself  as 
most  fortunate  in  having  been  able  to  complete  the  actual 
theory  of  the  steam-engine  at  work. 

A  step  in  the  right  direction  was  made  in  locating  the 
place  and  time  of  the  condensation  in  steam-cylinders  by 
M.  Leloutre. 

G.  A.  Hirn  {Theorie  Mecanique  de  la  Choleur,  1876, 
Vol.  ii.  page  55)  says : 

"  In  comparing  the  actual  cost  of  our  engines  per  stroke 
with  the  theoretic  cost  obtained  by  multiplying  the  volume 
opened  to  the  steam  by  the  density  of  this  vapor  supposed 
superheated,  I  always  found  the  first  result  very  much 
higher  than  the  second.  For  a  long  time  I  continued  to 
believe  that  this  increase  of  cost  arose  from  piston-leaks. 
These  leaks  seemed  to  me  both  natural  and  probable,  since 
we  were  working  (as  I  then  believed)  at  a  very  high  tem- 
perature, capable  of  destroying  or  evaporating  the  lubri- 
cants used  in  the  cylinder  to  diminish  the  friction  and  wear 
of  the  parts. 

"  I  yield  to  M.  Leloutre  the  whole  merit  of  having  op- 
posed these  views,  of  having  suggested  to  me  as  both  jiossi- 
ble  and  probable  the  existence  of  condensation  of  steam 
during  admission  resembling  a  loss  by  leakage,  and  giving 
to  the  steam  a  density  much  greater  than  would  be  obtained 
by  calculation.  I  yield  to  him  the  merit  of  having  in  a 
manner  forced  me  to  make  new  experiments  which  would, 
by  various  methods,  bring  the  truth  to  light." 

In  a  controversy  with  Zeuner,  Hirn  denies  the  possibility 


PREFACE.  7 

of  establishing  a  general  theory  of  the  steam-engine,  in  the 
following  words : 

"  To-day  my  conviction  remains  as  it  existed  twenty  years 
ago.  A  proper  theory  of  the  steam-engine  is  impossible. 
An  experimental  theory  based  upon  the  motor  itself  in  all 
the  forms  in  which  it  has  been  attempted  in  applied  me- 
chanics is  alone  able  to  lead  to  exact  results." 

The  method  of  treatment  used  by  the  writer  is  only  one 
of  many  which  have  been  relinquished  because  of  giving 
impossible  results  when  laboriously  elaborated  from  actual 
data  more  or  less  deficient  on  important  points. 

This  should  not  be  construed  as  a  complaint.  The  keen 
personal  delight  arising  from  the  discovery  of  new  truth 
would  have  compensated  for  far  more  toil  had  it  been  re- 
quired. 

So  far  as  he  knows,  the  writer's  method  is  new,  and  cer- 
tainly original,  and  has  been  adopted  mainly  for  the  purpose 
of  rendering  the  results  intelligible  to  those  who  are  actually 
engaged  in  the  designing  and  care  of  engines. 

It  has  shown  that  the  wide  differences  in  experimental 
results  of  tests  of  different  types  and  sizes  of  engines  are  not 
irreconcilable,  and  that  the  builder  of  small  engines  of  the 
non-condensing  type  is  quite  as  right  in  adopting  four  expan- 
sions as  the  builder  of  enormous  marine  engines  of  the 
compound  type  is  in  adopting  expansions  of  ten  or  more 
volumes. 

The  value  of  the  constant  of  condensation  is  not  so  accu- 
rately determined  as  we  could  wish,  and  will  require  further 
experiment.  It  probably  is  very  nearly  right,  and  cannot 
lead  users  astray  in  practice. 

There  is  no  test  of  an  incomplete  theory  or  superficial 
reasoning  like  an  experiment. 

The  mechanical  skill  of  Messrs.  Wheelock,  Reynolds,  and 
Harris  have  rendered  experiment  possible,  and  the  thorough 


8  PREFACE. 

and  careful  work  of  Mr.  Hill  in  making  the  experiments 
upon  them  has  placed  within  our  hands  results  which  should 
accord  with  a  proper  theory. 

The  supplementary  experiments  of  Messrs.  Gately  and 
Kletzsch,  although  not  so  accurate,  add  to  the  completeness 
and  breadth  of  the  proof  of  the  law  of  condensation.  They 
have  "builded  better  than  they  knew,"  and  deserve  ac- 
knowledgment for  their  services  and  industry. 

In  making  the  calculations  the  steam-tables  of  Mr.  Clias. 
T.  Porter  have  been  used.     (The  Kichards  Indicator.) 

The  author  regrets  the  length  of  some  of  the  formulae, 
caused  by  the  necessity  of  including  all  the  various  influ- 
encing conditions  in  one  expression.  However,  they  will  be 
found  to  be  very  easily  comprehended. 

Many  writers  and  experimenters  have  stated  and  proved 
the  advantages  of  expansion,  compression,  superheating, 
steam-jacketing,  high  speeds  over  slow  speeds,  large  engines 
over  small  engines,  high  pressures  over  low  pressures,  con- 
densing over  non-condensing  engines,  and  of  compounding 
cylinders ;  but  through  lack  of  a  sufficiently  thorough  quan- 
titative study  of  these  expedients  they  have  in  many  in- 
stances become  partisan  in  their  views,  and  have  drawn 
incorrect  general  conclusions  from  their  experiments  and 
reflections. 

It  has  been  the  wish  of  the  writer  by  a  careful  quantita- 
tive weighing  of  the  results  to  define  the  limitations  of  these 
various  expedients  and  to  enable  others  to  see  where  and 
how  they  should  be  used. 

In  this  departure  from  older  paths  the  writer  cannot  feel 
quite  sure  of  his  ground  on  all  points,  although  convinced 
of  the  practical  accuracy  of  his  theory  for  technical  uses, 
nor  does  he  lay  claim  to  infallibility ;  he  presents  his  facts, 
computations,  and  ideas  for  your  consideration  and  verifica- 
tion, asking  your  assistance  in  a  research  of  inestimable 


PREFACE.  9 

value  to  the  arts,  and  assuming,  not  the  attitude  of  one 
having  authority,  but  only  that  of  a  patient  student  of  the 
real  facts  of  the  action  of  Steam  inside  of  the  steam-cylin- 
der, as  derived  from  and  verified  by  the  most  reliable  ex- 
periments upon  the  steam-engine  accessible  to  him. 

It  has  been  thought  best,  though  publishing  this  in  a 
separate  book-form,  to  page  it  for  insertion  in  the  third  edi- 
tion of  The  Relative  Proportions  of  the  Steam- 
Engine,  of  which  it  properly  forms  one  chapter. 

W.  D.  M. 
University  of  Pennsylvania, 
Philadelphia,  1886. 


CONTENTS. 


CHAPTER  XVI. 


THE   LIMITATIONS   OF   THE   EXPANSION   OF   STEAM. 
Art.  Page 

73.  The  Influence  of  Condensation  Neglected 176 

74.  The  Influence  of  Initial  Condensation 185 

75.  Tlie  Law  of  Condensation  of  Steam  in  the  Steara-Engine 187 

76.  The  Influence  of  Compression 192 

77.  The  Constant  of  Condensation 195 

78.  The  Influence  of  Superheating. 196 

79.  The  Influence  of  the  Steam-jacket 204 

80.  The  Influence  of  the  Valve  Movement 204 

81.  Computation  of  Condensation 205 

82.  Probable  Errors  of  the  Table 208 

83.  The  Influence  of  the  Condenser 210 

84.  The  Jet-Condenser 211 

85.  The  Surface-Condenser 211 

86.  The  Law  of  Re-Evaporation  after  Cut-off" 213 

87.  The  Influence  of  Compounding  Cylinders 215 

88.  The  Relation  of  Cylinder  Ratio  to  Ultimate  Expansion 222 

89.  The  Influence  of  the  Receiver  and  Clearances 223 

90.  The  Horse-Power  of  Compounded  Cylinders 227 

91.  The  Influence  of  Cranks  at  Right  Angles 228 

92.  Condensation  in  Compounded  Cylinders 234 

93.  Methods  of  Experimentation 236 

94.  Code  for  Test  of  Boilers 236 

95.  Code  for  Test  of  Steam-Engines 241 


176 


THE  RELATIVE  PROPORTIONS 


CHAPTER    XVI. 

THE   LIMITATIONS   OF  THE   EXPANSION   OF   STEAM. 

(73.)  The  Influence  of  Condensation  Neglected. 

Fig.  32. 


Let  (IP)  =  the  desired  horse-power  of  the  engine. 

"  F  =  the  mean  effective  pressure  of  steam  in  cylinder 
in  pounds  per  square  inch. 

"  Pj  =  the  absolute  initial  pressure  of  steam  in  pounds 
per  square  inch. 

"  B  =the  absolute  back  pressure  of  steam  in  pounds 
per  square  inch,  exhaust  open. 

"  e  =  the  fraction  of  the  volume  of  the  steam-cylin- 
der at  which  steam  is  cut  off. 

"  b  =the  fraction  of  the  volume  of  the  steam-cylin- 
der at  which  exhaust  closes,  being  measured 
from  the  same  end  of  the  diagram  from  which 
e  is  measured. 

"  k  =  the  fraction  of  the  volume  Fof  the  steam-cylin- 
der allowed  for  clearance. 

"  V  =  the  volume  of  the  steam-cylinder,  inclusive  of 
one  clearance. 


OF  THE  STEAM-ENGINE.  177 

The  best  method  of  obtaining  the  volume  of  the  steam- 
cylinder  ( V)  and  the  clearance  (k)  is  to  fill  the  cylinder 
with  water  with  the  crank  on  the  most  distant  dead  point, 
and  then  to  fill  the  clearance  with  water.  The  weight  of 
water  in  the  clearance,  divided  by  the  weight  of  water  in  the 
whole  cylinder  and  clearance,  will  give  the  value  of  k.  Ref- 
erence to  the  diagram  (Fig.  32)  will  make  this  clear. 

The  mean  eflfective  pressure  = 
1     h' 


P-eP, 


1+nat.  log 


B 


1-b 


(l-nat.log-^| 


(218) 


For  a  cut-off  e  the  water  used  per  horse-power  per  hour  is 
approximately,  when  we  neglect  the  saving  by  compression, 
^_  859375  e 


s\ePJl+nsit.log---]-B  l-6(l-nat.'log-J    l(2i9) 

in  which  TT^  weight  of  water  evaporated,  and  ;S'= specific 
volume  of  the  steam  for  the  pressure  P^. 

Formula  (218)  is  stated  under  the  assumption  that  the 
curve  of  expansion  is  an  equilateral  hyperbola,  which  we 
will  show  to  be  approximately  an  average  of  good  indicator- 
cards. 

The  usual  thing  among  many  of  the  writers  of  the  present 
day  is  to  dismiss  the  isothermal  curve  with  a  condemnation 
and  to  make  use  of  the  adiabatic  curve,  but  unfortunately 
for  them  it  does  not  agree  so  well  with  the  actual  curve  of 
pressures  from  our  best  engines  as  taken  with  an  indicator 
as  does  the  isothermal  curve. 

It  will  be  observed  that  the  curve  of  expansion  used  is  the 
equilateral  hyperbola.  This  curve  coincides^  with  great  ac- 
curacy, with  the  best  results  derived  from  indicator-diagrams, 
and  we  can  therefore  safely  use  it  until  an  adiabatic  engine 
is  produced  for  our  discussion. 


178 


THE  RELATIVE  PROPORTIONS 


Reference  to  the  subjoined  diagrams  (Figs.  33,  34,  35,  36, 
37,  38),  which  are  all  taken  from  engines  of  excellent  work- 
manship not  embarrassed  by  sluggish  valve-motions,  will 
convince  the  reader  of  the  accuracy  of  this  statement. 


Fig.  33. 


Non-Condensing  Haebis-Corliss,  No.  14,  June  22,  7.45  a.m.    (J.  W.  Hill.) 


Fig.  34. 


Non-Condensing  Haebis-Corliss,  No.  28,  June  22, 11.15  a.m.    Thompson 
Indicator. 

The  broken  curve  is  an  equilateral  hyperbola  from  the  point  of  cut-off  in  each  case 
of  Harris-Corliss  Engine.     (J.  W.  Hill.) 


OF  THE  STEAM-ENOINE. 
Fig.  35. 


179 


CoNDENSiNQ  Harris-Corliss,  No.  27,  JUNE  21,  11.45  P.M.     (J.  W.  Hill.) 


Fig.  36. 


CJoNDB.vsiNG  Haruis-Coki.iss,  No.  34,  June  22,  1.30  a.m.     (J.  W.  Hill.) 


Fig.  37. 


Diagram  of  the  Eruwn  Engink.     Non-Condensiko.     (Taken  by  F.  \V.  Bacon.) 
The  broken  curve  is  the  equilateral  hyperbola.    Absolute  initial  pressure,  90  lbs. 


180  THE  RELATIVE  PROPORTIONS 

Fig.  38. 


w 


Diagram  of  Buckeye  Automatic  Evgine.    Koutinq  Jet-Condenser. 

The  solid  curve  above  is  tlie  adiabatic  curve,  and  the  broken  curve  below  is  the 

isothermal  expansion  curve,  traced  on  the  diagram  for  comparison,  and 

beginning  at  the  toe  of  the  diagram.     (J.  W.  Thompson.) 

Absolute  initial  pressure,  93  lbs. 

Equation  (219),  if  we  take  account  of  the  steam  saved  by 
compression,  becomes,  when  measurements  are  taken  from 
the  diagram, 

859375 /e-y^^"^' 
W= j^ ^^,  (219  a) 

in  which  B^  =  maximum  pressure  of  compression, 

and  Pc  =the  pressure  at  point  of  cut-off; 
or,  in  a  more  general  form,  not  quite  so  accurate  as  (219  a). 


859375 /e- 


tJ 


W f^ :.  (219  S) 

This  formula  is  more  accurate  than  (219). 
The  Warrington-Thompson  rule  is, 

^  ^  859375  (1-^  (219  c) 

in  which  S^  is  the  fraction  of  the  theoretical  stroke  (or  vol- 
ume inclusive  of  one  clearance,  F)  at  which  a  line  drawn 


OF  THE  STEAM-ENGINE.  181 

parallel  to  the  atmospheric  line,  at  a  height  equal  to  the 
terminal  pressure  of  expansion,  cuts  the  curve  of  compres- 
sion. S^  is  the  specific  volume  of  the  steam  for  its  terminal 
pressure. 

This  very  practical  and  simple  rule  had  its  origin  as 
stated  in  the  following  letter  from  Mr.  J.  W.  Thompson, 
Salem,  Ohio : 

"There  was  formerly  in  our  employ  a  young  man,  by 
namfe  Jesse  Warrington,  who  was  something  of  a  prodigy 
in  the  way  of  quick,  instinctive,  and  short-cut  mathematics. 
Away  back  in  the  '70s,  about  1874,  if  wx  mistake  not,  he 
suggested  to  the  writer  that  there  might  be  a  constant  fig- 
ured out  which,  when  divided  by  the  product  of  the  mean 
effective  pressure  and  the  volume  of  the  total  terminal 
pressure,  would  give  the  theoretical  rate  of  water  consump- 
tion, independently  of  any  knowledge  of  the  size  and  speed 
of  the  engine.  Acting  on  the  hint,  I  figured  one  out,  it 
being  obviously  the  consumption  of  water  per  indicated 
horse-power  per  hour  of  an  engine  subjected  to  one  pound 
maximum  eflficient  pressure,  and  driven  by  solid  water  in- 
stead of  steam.  The  process  was  as  follows :  A  horse-power 
being  33,000  foot-pounds  per  minute,  it  will  be  23,760,000 
inch-pounds  per  hour;  this  divided  by  27.648,  the  number 
of  cubic  inches  in  a  pound  of  water  when  a  cubic  foot 
weighs  62.5  pounds,  gives  859,375,  and  I  remember  being 
somewhat  struck  with  the  singular  fact  that  the  calculation 

,         ,1  .,,      ,     n     ,.        33,000x60x62.5 

comes  out  exactly  even,  without  a  traction.    — 

^  144 

also  gives  it." 

If  the  point  of  cut-oflT  is  easy  to  determine,  as  in  the  dia- 
grams of  properly -constructed  engines  already  given,  for- 
mulae (219),  (219  a),  or  (219  h)  may  be  used  as  the  judgment 
may  dictate. 

Should  it  be  impossible  to  determine  the  point  of  cut- 
is 


182  THE  RELATIVE  PROPORTIONS 

off,  then  the  Warrington-Thompson  rule  (219  c)  must  be 
used. 

Placing  an  indicator  on  the  steam-chest  will  show,  by  a 
sudden  jog  in  the  line,  the  point  of  cut-off,  or  reveal  defects 
or  sluggishness  of  valve-motions.     See  Fig.  39. 

The  quantity  of  steam  recorded  by  the  diagram,  if  de- 
duced by  the  Warrington-Thompson  rule,  is  simply  the 
amount  of  steam  remaining  as  vapor  in  the  steam-cylinder 
after  the  steam  has  done  its  work,  and  with  all  its  conveyed 
heat  it  is  immediately  thrown  away  through  the  exhaust- 
port. 

The  quantity  — ,  equation  (219  b),  is  quite  small  in  a 

non-condensing  engine,  and  should  never  exceed  the  clear anee 
k  in  value.  In  a  condensing  engine  it  is  usually  very  much 
smaller.  In  making  close  calculations  of  the  water  used, 
we  cannot  afford  to  neglect  this  quantity  ;  but  it  does  not 
sensibly  affect  the  point  of  cut-off. 

It  is  not  possible  to  avoid  initial  loss  of  heat,  to  construct 
an  engine  without  clearance,  or  to  obtain  a  perfect  vacuum  ; 
but  if,  for  the  purpose  of  obtaining  an  extreme  limit,  we 
neglect  these,  equation  (219)  becomes 

^= . : pounds  per  H.-P.  per  hour. 


^Pft  1  +  nat.  log 


The  following  table,  therefore,  gives  a  minimum  and  un- 
attainable quantity  of  dry  saturated  steam  for  each  atmos- 
phere up  to  12,  and  each  expansion  up  to  12.  The  fraction 
of  its  volume  at  which  the  steam  is  cut  off  will  be  found 
on  the  upper  horizontal  line  of  the  table,  and  the  steam- 
pressures  on  the  vertical  line. 


OF  THE  STEAM-ENGINE. 


183 


M     O     eo 


~»     OJ     o» 


Pressures  in  Atmos- 
pheres. 


rfk  -J  o  CO 


00  W   00  ts  to 
»>0   bi   X   r-"   hfi. 


5  o  S  o 

CO  CO  OS  w 

rfk  Ot  Ol  05 

K)  O  W  OJ 


CO  CO  CO  CO  rfi.  *• 

-J  QO  00  »  O  -^ 

-I  CO  O  iT  CO  CO 

-4  CO  4^  l-i  4.  en 


05i 


P  g  g  ,«  2:  ?S  ?g  ^    p  p  .^  tS 

00  tc  c»  o  bi  o  *-  o  it'  o  C5  bi 

COCO*.Ci>f'COC5M^-I4>.-l)*. 

i-il-'l-'l-il-l^V-l—il-'lOtOK) 
^   ;-J   00   00   CO   00   JO   p   p   p   p   p 

O      00      H-i     CO      CI      O      J-"     '.P»     i~»      o     I*^     o 
COC50«lCObO-40-lC500CO 

{;fc[t».jf»._rf>.cncncnj;icnppsp 
k)    If>.    b>    bo    b     K)    *>*>.    C5    b     H-i    bi    o 

tOl-'OOCOO-^OOlOOMCO 
tOh3t3COC0C0C0CO4^.^>f>.)f>- 

§  g  '^  g  is  b  S  2  8  S§  S  8 

_»-._— I  —  j-i  to  to  JO  ;c  to  CO  CO  CO 
Ifk  br  ^  b  b  io  if.  b  bo  b  io  b 

S^ocni-'ooolScocoiocsio 

p       p       P       h-i       H-i       >-'>-'»-'       ^       JO       JO       to 

b     bo     b     M     CO     'rfk     b     bo     b     >-'     if>-    ^ 

OCO-~ICOOOOCOO«OC3IOCO 

p   p   p   p   p   p    r^   .—    ?   r"   r"   ?* 

Ij     to    i^    bi    ^    bo     b    *-■     CO     b     ^    b 

t0-4OCJll-'-4l>S00C5C0-405 
p       p       p       p       p       p      p       p       p       _-•       ►-'       ;-• 

b     b     b     b     to     t^.    bi     -I     bo     b     to     b 

WitOCnOCnr-'tfk.O-^COCirfi. 

pppppppppppj-i 

CO    If».    b    ^    bo    b     f-"    b     >ti    b    b    I-" 
coosooio-itocjio-Jtorf^"-' 


5®    J*    5° 

If.       03       00 


t&  §; 


p  p 

^    b 

o    CO 


p    p 

en     ^ 

o    oi 


o    <»    o 


8   g 


g  8 


p  p 

to    b 
o     to 


O      CO 

h  8 


p     p 

b     io 
Ot     o 


to    to     to    CO 


IS 


Pressures  in  Lbs. 
per  Square 
Inch  (Abs.). 


S3 


r}^ 


.So        Specific  Volumes. 


t 


►1 


184  THE  RELATIVE  PROPORTIONS 

Inspection  of  this  table  will  show  how  rapid  the  increase 
of  economy  due  to  expansion  appears  to  be  up  to  about  10 
expansions,  where  gain  by  this  expedient  becomes  compara- 
tively small  with  subsequent  increase. 

The  first  vertical  column  shows  also  the  slower  gain  due 
to  increased  pressures  up  to  12  atmospheres ;  this  gain  is  of 
great  practical  value,  as  the  steam  appears  to  be  drier  at 
high  pressures  and  the  engine  becomes  more  powerful  for  a 
given  volume  of  cylinder. 

The  formula  (217)  given  in  the  preceding  chapter  will 
give  the  uttermost  limit  attainable  under  the  assumptions 
made  for  this  table. 

It  is  easy  to  see  that  so  long  as  steam  expands  according 
to  Marriotte's  law,  when  acting  inside  of  a  steam- cylinder, 
and  we  are  restricted  to  moderate  pressures,  we  cannot  hope 
to  obtain  a  horse-power  per  hour  for  less  than  one  pound  of 
coal. 

The  cost  of  power  may  be  divided  into  two  accounts : 

The  first  is  the  constant  charges,  which  are — 

(1)  Interest  on,  deterioration  of,  and  repairs  to  engine. 

(2)  Wages  of  firemen  and  engineer. 

(3)  Cost  of  oil  and  waste. 

(4)  Interest  on,  deterioration  of,  and  repairs  to  boilers. 

(5)  "  «  «  shelter  if 
separate. 

(6)  Taxes  and  insurance  on  engine  and  boilers. 

The  second  is  the  cost  of  the  fuel  and  water  required  to  pro- 
duce and  also  condense  the  steam  per  horse-power  per  hour. 

The  constant  charges  may  within  narrow  limitations  be 
regarded  as  proportional  to  the  power  required.  As  the 
power  required  becomes  larger  the  proportion  between  the 
constant  charges  and  the  power  becomes  smaller,  provided 
we  obtain  it  from  one  engine  of  not  too  expensive  construc- 
tion or  size. 


OF  THE  STEAM-ENQINE.  185 

(74.)  The  Influence  of  Initial  Condensation.— The 

cost  of  fuel  and  water  required  is  divided  into  two  parts : 

(1)  The  amount  of  steam  appearing  from  the  diagram. 

(2)  The  amount  of  steam  lost  by  condensation  in  the 

steam-cylinder. 

The  losses  in  heating  the  water  in  the  boiler  and  in  con- 
veying the  steam  to  the  engine  are  not  properly  chargeable 
to  the  engine,  and,  being  an  item  for  which  separate  provision 
must  be  made,  will  not  be  regarded. 

The  intending  purchaser  must  first  fix  upon  that  size, 
speed,  and  type  of  engine  which  \\i\\  give  him  the  power  he 
requires  for  the  least  cost  in  steam,  and  then  obtain  that 
engine  for  the  least  sum  possible. 

Cases  may  and  do  occur  in  which  the  different  types  of 
engines  vary  enormously  in  cost. 

In  such  cases  there  is  but  one  way  to  decide.  A  detailed 
calculation  of  the  constant  charges  and  the  cost  of  steam 
must  be  made  for  each  engine,  and  that  engine  showing  the 
least  sum  per  horse-power  per  hour  will  be  the  proper  one. 

It  may  occur  that  greater  cost  of  steam  per  horse-power 
per  hour  will  be  recouped  by  a  lesser  constant  charge  per 
horse-power  per  hour. 

It  is  never  safe  to  guess,  and  particular  attention  should 
be  paid  to  the  cost  of  condensation  of  steam  when  a  con- 
denser is  used. 

We  can  then  write  the  following  equation  for  discussion  : 

Work 


Cost  of  work  in  steam' 
or,  for  one  stroke  of  the  engine, 

Mean  effective  pressure  X  Volume  of  steam-cylinder 


r= 


Cost  in  [Indicated  steam  +  Initial  condensation  +  Final  condensation  of  steanij 

The  final  condensation  of  the  steam  ordinarily  requires 

16* 


186  THE  RELATIVE  PROPORTIONS 

some  of  the  power  in  the  engine,  and  demands  an  additional 
outlay  for  condenser  and  a  large  quantity  of  water. 

Where  water  is  costly,  this  may  result  in  a  decision  in 
favor  of  a  non-condensing  engine. 

The  whole  matter  of  final  condensation  is  one  for  a  calcu- 
lation and  comparison  subsequent  to  the  preliminary  calcu- 
lations of  the  steam  required  per  horse-power  per  hour  as 
delivered  by  the  boiler. 

We  can  then  reduce  the  above  equation  to  the  form. 


F= 


Mean  effective  pressure 


Indicated  steam  +  Initial  condensation 


The  indicated  steam  shown  by  the  diagram  to  exist  as 
vapor  in  the  engine-cylinder  has  already  been  discussed  at 
length. 

There  remains  for  our  consideration  the  initial  condensa- 
tion. 

In  order  to  establish  a  clear  understanding,  let  us  carefidly 
follow  the  steam  in  the  cylinder  through  one  stroke. 

The  order  of  events  would  seem  to  be  as  follows,  the 
engine  having  attained  its  regular  speed,  and  the  cylinder 
an  average  heat : 

The  entering  steam  touching  the  interior  of  the  cylinder 
condenses  very  rapidly  and  warms  it  up  to  the  temperature 
of  the  steam ;  this  warmth  proceeds  to  a  depth  proportional 
to  the  depth  already  cooled  by  the  exhaust ;  the  steam  then 
expands  after  cut-off,  falling  in  temperature  and  losing  heat, 
first  by  warming  up  the  cooled  cylinder-walls,  secondly  in 
doing  work ;  however,  the  heated  iron  of  that  part  of  the 
cylinder  exposed  before  cut-off  gives  up  heat  and  vaporizes 
the  condensed  water  of  initial  condensation  in  the  attempt 
to  equalize  the  temperatures  throughout  the  cylinder,  which 
is  effected  by  a  transfer  of  condensation  following  the  motion 
of  the  piston -head. 


OF  THE  STEAMENGINE.    i, -,  ,,  187 

At  the  end  of  the  stroke  the  temperature  of  the  whole 
iuteriial  surface  and  of  the  steam  is  that  of  the  terminal 
pressure,  the  steam  having  really  expanded  with  fresh  acces- 
sions of  heat  and  of  vapor  from  that  part  of  the  cylinder 
exposed  to  initial  steam ;  that  is,  exposed  before  the  cut-off 
occurs. 

Next  in  the  order  of  events  the  exhaust  opens  and  the 
whole  interior  of  the  cylinder  is  exposed  to  the  temperature 
of  the  exhaust,  the  piston  and  cylinder-head  being  exposed 
on  an  average  twice  as  long  as  the  cylinder-walls. 

In  every  engine  these  changes,  whatever  they  may  be, 
establish  an  equilibrium  among  themselves,  and  the  result  is 
that  a  certain  uniform  quantity  of  heat  is  lost  at  each  stroke, 
provided  the  thermal  value  of  the  steam  does  not  vary. 

As  long  as  we  know  the  equilateral  hyperbola  to  be  an 
average  of  the  curves  produced  by  good  indicators  on  good 
engines,  the  condensation  of  steam  during  expansion  or  its 
re-evaporation  is  of  minor  importance,  and  we  can  return 
to  the  initial  condensation  of  steam  for  the  present. 

It  is  nonsense  to  discuss  the  curve  of  adiabatic  expansion 
until  we  can  produce  adiabatic  engines. 

The  first  step  in  the  quantitative  investigation  of  the  con- 
densation of  steam  is  the  establishment  of  a  standard  or 
constant. 

We  will  assume  this  to  be  the  weight  of  steam  con- 
densed PER  minute  in  raising  THE  TEMPERATURE  OF 
A  SURFACE  OF  CAST  IRON  OF  ONE  SQUARE  FOOT  AREA 
ONE    DEGREE    FAHRENHEIT. 

This  weight  can  be  converted  into  heat-units  by  multiply- 
ing it  by  the  total  heat  of  steam  less  heat  of  its  water  for  the 
given  pressure  at  cut-off*. 

(75.)  The  Law  of  Condensation  of  Steam  in  the 
Steam-Engine.— The  loss  of  heat  by  the  steam  in  the 
cylinder  is  proportional  to — 


188  THE  RELATIVE  PROPORTIONS 

I.  The  difference  of  temperatures  of  the  steam  at  the 
point  of  cut-off  and  while  being  exhausted. 

II.  The  area  of  cast  iron  exposed  to  the  entering  steam 
up  to  the  point  of  cut-off. 

III.  The  time  of  exposure  of  the  interior  surface  of  the 
steam-cylinder  to  the  exhaust  steam. 

IV.  It  is  reduced  by  compression  subject  to  the  same  laws, 
but,  as  this  is  quite  a  small  quantity  in  most  cases,  we  will 
neglect  it  for  the  present. 

To  the  notation  already  in  use  let  us  add : 

Tj  =  temperature  of  steam  at  point  of  cut-off. 

T«  =  temperature  of  steam  during  exhaust. 

N  =  number  of  strokes  of  engine  per  minute. 

C  =  the  constant  of  condensation. 

The  first  factor  (T^j-  T^)  can  at  once  be  written. 

Assuming  the  crank  to  have  uniform  rotation,  and  the 
angle  which  it  forms  with  the  centre  line  of  the  steam-cylinder, 
measured  from  the  end  from  which  it  is  retreating,  to  be  a. 

If  we  take  account  of  the  variable  time  of  exposure  of 
the  cylindrical  walls  of  the  cylinder,  as  also  of  the  variable 
value  of  the  area  of  the  cylindrical  elements,  we  have  for 
the  time  of  exposure  to  exhaust,  multiplied  by  the  area. 

For  the  piston-head  and  the  cylinder-head,  and  the  clear- 
ance which  is  neglected. 

For  the  variable  area  for  each  increment  of  the  angle  «, 
the  crank  being  assumed  to  have  a  uniform  rotary  motion, 

{-d)ds  =  +  (ttcZ)-  sin  ada. 

A 

For  the  variable  time — -  of  exposure  to  exhaust  of 

180iV^  ^ 

each  element,  {jzd)d8.     For  their  product 

^- — ^-  sm  aaa. 

2iY   180 


OF  THE  STEAM-ENGINE. 


189 


For  the  product  of  time  and  area  of  interior  of  cylinder, 
between  limits, 

a  =  180= 
d+-  " 


2N 


180 


a  sin  ada 

a  =  cos-1  (  2e  —  1 


but,    j    a  sin  ada  =sm  a  —  a  COS  a  =  |/1  —  cos'^  a  —  a  COS  a, 

for  a  =  180°  we  have  tt, 

for  a  =  cos"^  (2e  —  1)  we  have 

V^l-(2e-l)!(2e  - 1)  cos"^  (2e  - 1). 

Therefore  we  have,  as  a  final  quantity  for  any  cut-off  e, 


2N 


(^+-;7r-|/l-(2e-l/  +  (2e-l)cos-H2e 


^.„]. 


This  latter  expression  should  be  multiplied  by  (Ti—  T^ 
and  the  constant  of  condensation  C,  giving  for  the  total 
condensation  during  one  stroke  and  without  compression. 


{-^--)l^.H 


TT— 1/1— (2e— l)a + (2e— 1)  cos-l(2e 


-«}}" 


(220) 


We  also  have  for  the  combined  time  and  area  of  exposure 
of  initial  steam,  or  putting  h  for  e  of  compressed  steam. 


^j-cos-ni-2e)+- 

2N  i^         ^  ^ 


l/l  -  (l-2e)^  -  (1-e)  cos-^(l-2e) 


h 


but  this  is  a  lesser  and  not  the  controlling  quantity. 
Tracing  the  curve  of  condensation, 

r=l_  1  I  v/l-(2e-iy-h(2e-l)  cos-^(2e-l). 

If  in  this  equation  we  make  e  the  independent  variable, 
it  represents  a  long,  easy  curve  which  approximates  very 
closely  to  a  straight  line  from  e-0.15  to  0.5. 


190 


THE  RELATIVE  PROPORTIONS 


We  have,  as  shown  in  the  diagram,  values  of  I^as  ordi- 
nates  for  each  abscissa  e  to  unity. 


e 

.« 

^ 

*     T/te   Cttive  0/  Con  tiert^ftf^fti^^ 

0^ 

/.ooo 

O-f  S^iea  7it  in  ^n^'          ^,^^^:^^:^ 

OjSX' 

^1 

acst 

^/*- 

C 

^ 

^iW- 

^ 

\                   ^^ 

aioi 

^ 

f. 

"ai^Y 

I 
^ 

( 

a/ 

o.x, 

as 

^^  . 

OJ- 

0.9 

«V 

0.8' 

Gff 

f. 

Between  the  limits  e  =  .15  to  e  =  .55  the  equation  of  the 
nearly  coincident  straight  line  is 

F=e  + 0.194. 
Equation  (220)  becomes 


C 


(T.-T.)f^(^UY.) 


or  between  the  above  limits  for  e  approximately. 


of  cut-off  is 


I  steam  in  the 


+  \e  +  .ld4:\s 


^^ 


(221) 


(221  a) 


The  weight  of  steam  in  the  form  of  vapor  at  the  moment 
62. 


(222) 


Neglecting  losses  due  to  pipe-condensation  and  priming, 
and  the  gain  due  to  compression,  and  adding  to  this  the 
weight  of  condensed  steam  in  the  cylinder  at  the  moment  of 

62.5 


cut-off,  we  have 


S 


eV+G 


{n-T)§{d.Ys) 


=  w. 


or,  between  limits  set  above,  F=e+.194. 


OF  THE  STEAM-ENGINE.  191 


TT.  .      SC 

=  r  =  1  + 


(^'-}!t-^)  ^-) 


W  Q2.5N 

in  which  J  and  s  are  measured  in  feet. 

Let^=^and  D  =  2^^a 

S  N 


D  1/1  ^  e+.194\ 
A  e\s  d      I 


Wehaver  =  l+^-  -+^^4P^  •  *        (223a) 


These  equations  give  us  a  means  of  determining  from  the 
indicator-card  the  steam  actually  furnished  by  the  boiler. 

Presuming  the  value  of  C  to  be  known,  and  dry  saturated 
steam  used,  we  can  predict  the  most  economical  expansion 
for  any  size  of  cylinder,  number  of  strokes,  pressure  of 
initial  steam,  and  back  pressure  during  exhaust. 

If  we  desire  to  know  the  practically  most   economical 
number  of  expansions,  or  its  inverse,  the  true  point  of  cut- 
off, we  must  find  the  maximum  of  the  following  equation : 
_     PV     _  P 

^       62.5   T.    Are 
r-eV 

Neglect  clearance  and  compression  in  the  value  of  P,  and 
substitute  for  r  its  value,  we  have 

ePJl+nat.  W-)-^ 


(l+nat.  log-j 


Differentiating  with  respect  to  e  for  a  maximum,  we  have 

P  ,/l  ,  .194\     Dd         ^  T      1  ,oo^A 

6!  =  — -+/-  +  — --—; — -nat.  log-  (224) 

Pi   \s      d   ]  Ad^-D  ^  e  ^       ^ 

This  most  important   transcendental   equation  must  be 
solved  tentatively ;  or  we  can  assume  a  value  for  e  which 

must  always  be  greater  than  — ,  and  deduce  the  most  eco- 

Pb 


192  THE  RELATIVE  PROPORTIONS 

nomical  ratio  of  stroke  to  diameter  of  steam-cylinder.  This 
equation  is  not  exact  when  e  is  less  than  .15  or  exceeds  .50, 
which  is  not  a  usual  thing. 

(76.)  The  Influence  of  Compression. — If  we  take 
account  of  clearance  and  compression,  we  have 

ePJl  +  nat.  log ---\ -jB/I-jBHi -nat.  log  ^ 


Differentiating  for  a  maximum,  we  have 


B 


(■   '    ' r  nat.  log  -• 
1       .T94\ 


e  = +  i  + , r  nat.  log  -•  (224a) 

P.  /  .  - 

D 


A  + 


Assuming  b  and  ^  =  0,  we  obtain  equation  (224). 

Use  equation  (224)  to  obtain  an  approximate  value  of  e, 
and  substitute  in  (224  a)  to  obtain  an  accurate  value  when 
clearance  and  compression  are  to  be  considered. 

The  compression  of  the  steam  by  early  closing  of  the  ex- 
haust-port has  two  effects :  it  diminishes  the  power  of  the 
engine  and  increases  its  economy  by  saving,  at  each  stroke, 
an  amount  of  steam  which  fills  the  clearance  at  the  maxi- 
mum compression  pressure  -S^.  May  it  not  also  diminish 
the  amount  of  initial  condensation  of  steam  by  covering 
the  surfaces  of  the  piston-  and  cylinder-heads  with  films  of 
water  at  a  temperature  determined  by  the  maximum  com- 
pression pressure  of  saturated  steam  and  the  time  of  ex- 
posure? The  barrel  of  the  cylinder,  near  the  end,  may 
also  have  a  preliminary  warming,  due  to  the  hyperbolic  in- 
crease of  pressure  of  the  steam  from  the  moment  of  exhaust- 
closure. 


OF  THE  STEAM-ENGINE. 


193 


The  following  pair  of  diagrams  will  illustrate  (Fig.  39) 
the  case  just  stated. 

Fig.  39. 

I         iBoiler . 


Porter-Allen  Engine.    Post-Office  Building,  Philadelphia,  March  30,  1884.    Scale, 
40  Pounds  per  Inch. 

Steam  not  tested,  but  not  superheated. 

Valves  and  piston  not  tested. 

Engine  non -condensing. 

Stroke,  2^  =  2  ft. 

Clearance,  4?  per  cent,  of  stroke  =  0.09  ft.  deduced  from 

expansion  curve. 
Diameter,  14^  =  1.208  ft. 
Abs.  initial  pressure,  back  end,  87  lbs. 

front   "     89   " 

mean,        88   " 
"    back  pressure  at  midstroke,  16   " 
Temperature  of  initial  steam,  318.45°  Fahr. 
Specific  vol.  of      "  "        300.8. 

Temperature  exhaust      "        216.29°  Fahr. 
Number  of  strokes,  400  per  minute. 
Mean  eff.  pressure,  front  end  =  20.62  ^   . 

"       "         "  back    "    ^^rj^^l^r^^^^^^  y-oi^^'J'^^- 

"       "         "  mean        =18.93)         ^^^^^  ^«^<i- 

Indicated  horse-power  =  74.91. 

17 


194 


THE  RELATIVE  PBOPOBTIONS 


Maximum  back  pressure  =  pressure  at  cut-off. 

(e)  Point  of  cut-off,  front  end  |  ^^^  .^^g  ^^^^  ^^^^^^ 

"      back    "    J 
(k)  Clearance  (true),  0.043. 

Cut-off  less  compression  (e  —  Jc),     0.125  =  i. 


Indicated  steam, 


859375 


18.86  lbs.  per  horse-power 


300.8x18.93x8 

per  hour. 

Let  Tc  =  the  temperature  Fahrenheit  due  to  maximum 
compression  pressure,  then  formula  (220)  becomes,  when  we 
neglect  the  time  of  exposure  to  compressed  steam. 


(  ^^~^'  )'S  +  (^*~^''  )  §^U-V^-(^^^y'  +  (2«-l) co8-l(2e-l) 


(2205) 


or,  simplifying  as  before. 


C 


2\-Z 


d+  [n-T?\(,194.  +  e)s^  ~    (220c) 

If  the  maximum  compression  pressure  becomes  equal  to 
the  pressure  at  cut-off  Tj,  =  T^,  assuming  pressures  and  tem- 
peratures to  vary  together,  giving  for  the  condensation 
within  .50  per  cent,  cut-off 


T,-Z 


(.194  +  e)7rc^g 

2N 


(220  d) 


Equation  (223),  using  the  value  given  for  condensation 
by  (220  c),  becomes 

'-'*5iF[(«-''-)l*f'^'(«-''->].(^-»' 

or,  if  maximum  compression  pressure  equals  pressure  at 
cut-off, 


r  =  l  + 


JIC_  (\2(e  +  .lM)^       (223  c) 
62.5NV'     ^V       erf 


or, 


1+- 


1  —  6(1  — nat.  log 


OF  THE  STEAM-ENGINE. 
D  (e  +  .194) 


de 


+  i  + 


195 
(223  c/) 


— -  nat.  log  -  ;   (224  h) 


"6  ^  +  -  +  .194 

d  de2 

A  =  — ,  and  the  factor  -» disappears  from  formula.     (224  a) 

If  compression  to  initial  pressure  does  prevent  condensa- 
tion by  the  piston  and  cylinder-heads,  (223  d)  is  a  minimum 
value. 

It  is  probable  that  in  most  cases  where  clearance  and  com- 
pression are  slight  the  saving  of  condensation  is  small  from 
compression,  owing  to  lack  of  time.  In  cases  of  large  clear- 
ances and  early  compression  the  time  of  exposure  is  suf- 
ficient to  enable  warming  of  piston  and  cylinder-heads  by 
condensation  of  the  compressed  steam. 

(77.)  The  Constant  of  Condensation.— In  order  to 
prove  the  value  of  C  to  be  constant  under  all  conditions 
existing  in  steam-engines,  we  must  refer  to  practical  experi- 
ment. 

In  its  most  exact  form  we  can,  from  equations  (223)  and 
(220  6),  write 


C 


''4'-'^){' 


1  Ly 


2S 


(t.-tYj{t.-z)^ 


(225) 


For  a  cut-off  not  greater  than  .50  or  less  than  .15,  we  have, 
approximately, 

''-^  .(225a) 


2^ 
62^eN 


^t.-tY-^^t.-t^-^ 


196  THE  RELATIVE  PROPORTIONS 

Without  compression  being  used, 

0=- ^ ''-^ =r.        (225  6) 


2S 


(.._.. )(i,^B) 


Unless  the  compression  of  the  steam  is  very  marked,  it 
will  have  little  effect  in  reheating  the  piston-  and  cylinder- 
heads,  and  the  exhaust  temperature  T^  must  be  used.  AVith 
even  slightly  leaky  steam-valves,  the  compression  line  is 
mainly  due  to  a  drizzle  of  steam  into  the  cylinder  after  the 
exhaust-port  is  closed,  and  to  the  lead,  and  not  to  the  steam 
entrapped  by  the  closing  of  the  exhaust-ports. 

With  compression  to  initial  pressure  and  large  clearance 
we  may  have  more  nearly 

r-1 


2^ 


62hN 


(r.-r.){^) 


(225  c) 


(78.)  The  Influence  of  Superheating.— As  some  of 
the  experiments  which  will  be  discussed  in  a  subsequent 
table  were  said  to  have  been  made  with  siiperheated  steam, 
it  will  be  necessary  to  form  an  opinion  as  to  its  action  inside 
of  the  steam-cylinder. 

This  is  a  difficult  undertaking,  and  the  reader  must  use 
his  own  judgment  in  deciding  whether  or  not  to  adopt  the 
opinions  put  before  him. 

Superheating  steam  has  two  consequences.  The  temper- 
ature of  the  steam  is  increased  beyond  its  temperature  of 
saturation,  and  its  specific  volume  is  increased  at  the  same 
time. 

The  behavior  of  the  iron  of  the  cylinder,  as  well  as  the 
mechanical  conditions  of  the  introduction  of  the  steam  into 
it,  will  not  permit  us  to  accept  the  results  of  calculation 


OF  THE  STEAM-ENGINE.  197 

under  other  circumstances  than  those  actually  existing  in 
the  engine  itself. 

The  following  suggestions  will  reveal  why  we  cannot  ex- 
pect superheated  steam  to  act  in  an  iron  cylinder  as  it  would 
in  an  adiabatic  vessel. 

If  the  steam  condenses  only  as  it  comes  in  contact  with 
the  walls, — that  is,  condenses  as  a  piece  of  ice  melts,  on  the 
outside, — the  main  body  of  the  steam  will  remain  superheated, 
and  successive  layers  of  steam  on  the  outside  be  condensed, 
until  the  walls  are  of  the  same  temperature  as  its  temper- 
ature of  saturation,  after  which  the  superheated  steam  would 
strive  to  re-evaporate  the  condensation,  and  the  iron  to  keep 
it  condensed  and  add  more  to  it,  with  all  the  advantage  on 
the  side  of  the  iron.  Since,  if  we  assume  steam  of  an  aver- 
age specific  volume  of  300,  their  comparative  weights,  volume 
for  volume,  are, — iron,  2160;  steam,  1;  and  as  the  specific 
heat  of  steam  is  0.48,  and  that  of  iron  0.12,  we  see  that,  vol- 
ume for  volume,  or  layer  for  layer,  iron  will  take  540  times 
as  much  heat  as  steam.  So  we  see  the  iron  will  not  only 
keep  what  it  has  condensed,  but  will  add  more  to  it  by  con- 
ducting the  heat  from  the  film  of  water  upon  it  away  so 
rapidly  as  to  cause  additional  condensation  in  the  adjacent 
layers  of  steam,  which  have  comparatively  no  conducting 
power  at  all,  if  we  can  draw  any  inference  from  the  ease 
with  which  priming  occurs  in  steam,  and  the  suspension  of 
globules  of  water  during  expansion  of  steam. 

The  advantages  of  superheated  steam  will  be  found  to  be 
in  the  more  complete  re-evaporation  during  expansion  leav- 
ing a  drier  cylinder,  and  consequently  less  to  be  evaporated 
by  the  heat  of  the  cylinder  during  the  exhaust,  which  will 
therefore  be  cooled  to  a  lesser  depth. 

It  is  not  surmised  that  the  temperature  of  the  iron  of  the 
steam-cylinder  rises  above  the  temperature  of  saturated 
steam  of  the  initial  pressure;  but  the  possibility  is  sug- 

17* 


198  TEE  RELATIVE  PROPORTIONS 

gested  that  the  iron  gets  more  heat  in  proportion  to  the 
superheating,  and  therefore  re-evaporates  the  steam  more 
readily  and  thoroughly.  Certainly  it  would  not  appear,  in 
the  table  of  the  Harris-Corliss  engine  condensing,  that  QQ 
per  cent,  of  the  indicated  steam  should  be  condensed  at 
cut-off,  or  with  the  same  engine  non-condensing  56  per  cent, 
of  the  indicated  steam  should  have  been  condensed  at  cut- 
off, if  all  the  superheating  of  the  initial  steam  had  not 
vanished  before  expansion  began. 

Neither  does  it  appear  from  the  diagrams  that  the  super- 
heating had  the  effect  of  raising  the  expansion  curve  above 
an  equilateral  hyperbola  in  the  Harris  and  other  engines, 
nor  does  w^et  steam  seem  greatly  to  modify  the  expansion 
curve  of  the  Brown  and  Porter-Allen  engines. 

The  fact,  how^ever,  is  undeniable  that  the  amount  of  heat 
conducted  away  is  proportional  to  the  conductivity  and  heat- 
capacity  of  the  iron  cylinder,  and  we  are  told  that  this  loss 
is  directly  proportional  to  the  difference  of  temperatures. 

It  is  worthy  of  note  that  the  superheated  steam  in  the 
Harris-Corliss  and  other  engines  must  have  instantly  be- 
come very  w^et  steam  upon  its  contact  with  the  cylinder ; 
and  therefore  if  damage  is  done  by  superheated  steam,  its 
evil  effects  wdll  appear  upon  the  valve-motion  and  upon 
lubricants  fed  through  the  steam-pipe. 

It  would  seem  as  if  especial  care  given  to  the  jacketing 
of  the  cylinder-barrel  would  be  almost  useless  trouble  until 
we  have  suppressed  initial  condensation  due  mainly  to  the 
piston-  and  cijlinder-heads. 

Even  were  we  to  obtain  very  good  non-conducting  sur- 
faces for  these  latter  parts,  it  is  doubtful  if  a  film  of  water 
would  not  appear  on  them  and  demand  conversion  into 
steam  at  the  beginning  of  each  stroke. 

Possibly  the  greater  economy  of  actual  steam  which  it  is 
claimed  uniformly  results  from  superheated  steam  lies  in 


OF  THE  STEAM-ENGINE.  199 

the  certainty  of  dry  saturated  initial  steam,  the  greater  cer- 
tainty of  more  complete  re-evaporation  during  expansion, 
and  the  presence  of  less  water  on  the  interior  walls  of  the 
steam-cylinder  demanding  re-evaporation  during  exhaust 
than  would  occur  with  saturated  steam. 

Practically,  superheating  is  often  done  with  the  waste 
gases  of  combustion,  and  therefore  costs  nothing  for  fuel. 
Because  what  is  called  saturated  steam  is  not  always  dry, 
we  should  not  jump  to  the  conclusion  that  under  all  cir- 
cumstances it  is  the  best  plan  to  use  superheated  steam. 

Let  us  essay  to  follow  the  interaction  of  superheated  steam 
and  the  iron  cylinder  walls  from  the  moment  of  its  entrance 
to  the  point  of  cut-off. 

At  the  moment  of  entering,  the  superheated  steam  fills 
the  clearance,  forming  a  thin  disk  of  vapor  between  two 
circular  iron  plates  (the  cylinder-  and  piston-heads)  of 
many  degrees  lower  temperature.  As  it  touches  the  iron  it 
first  parts  with  its  superheat,  and  then  condenses  copiously 
upon  these  surfaces,  and,  so  long  as  the  pressure  is  not  less- 
ened, the  iron  will  not  permit  re-evaporation,  although  the 
surfaces  may  be  streaming  with  water. 

Hirn  (Vol.  ii.  page  62,  Theorle  Mecanique  de  la  Chaleur) 
thus  describes  the  action  of  superheated  steam : 

"  In  a  cylinder,  at  the  moment  of  admission,  it  is  possible, 
and  it  ought,  to  stream  with  water  upon  the  walls ;  whilst 
the  free  space  should  be  filled  with  steam  of  231  Centigrade 
degrees  (the  temperature  of  his  superheated  steam). 

"  The  condensation  during  the  admission,  as  well  as  the 
evaporation  of  a  part  of  the  water  during  expansion,  takes 
place  by  contact,  part  by  part,  and  not  by  the  cooling  or 
heating  of  all  the  mass  present." 

From  the  narrow,  long  orifice  of  the  port  at  the  side  of 
the  cylinder  this  steam  passes  in,  frequently  at  the  rate  of 
a  mile  a  minute,  and  must  create  strong  swirls  and  eddies, 


200  THE  RELATIVE  PROPORTIONS 

thus  giving  the  superheated  steam  opportunity  to  come  in 
contact  with  the  streaming  walls  and  part  with  its  superheat. 

The  slow  motion  of  the  piston  at  the  beginning  of  the 
stroke  favors  this  action,  for  it  requires  one-third  of  the 
time  of  the  stroke  for  the  piston  to  reach  one-fourth  of  its 
travel. 

The  tendency  of  the  superheat  is  to  re-evaporate  the 
moisture  of  the  walls ;  and  of  the  iron,  to  take  the  heat  from 
this  film  of  water,  and  the  iron  probably  does  it  before  it 
can  re-evaporate.  Perfect  quiescence,  as  of  melting  ice,  is 
necessary,  to  accept  the  statement  of  Hirn  as  regards  the 
entire  retention  of  superheat  by  steam. 

It  is  more  than  probable  that  superheated  steam  will  part 
with  its  extra  heat  to  the  water  wherever  it  comes  in  con- 
tact with  it.  The  exact  action  of  the  film  of  water  inter- 
posed between  the  steam  and  the  iron  cannot  be  stated,  but 
it  is  probably  a  very  good  non-conductor  of  heat  to  the 
iron  from  steam  when  saturated. 

The  expressions  (220)  and  (220  a)  give  the  amount  of 
heat  demanded  by  the  iron  of  the  cylinder  before  it  will 
permit  the  steam  to  do  its  work. 

The  advantage  of  superheated  steam  lies  in  this :  First. 
Superheating  costs  little  additional  fuel.  Second.  The  iron 
takes  just  as  great  a  quantity  of  heat  as  with  saturated 
steam  of  the  same  pressure ;  but  the  superheat  satisfies  this 
requisition  in  part,  and  less  weight  of  saturated  steam  is 
required  to  drive  the  piston  ahead. 

Zeuner,  in  his  "  Theory  of  Superheated  Steam,"  Zeitschrift 
des  Vereins  Deutsches  Ingenieure,  Band  XI.,  1866,  gives  the 
following  formula  for  the  specific  volume  of  superheated  or 
saturated  steam  for  any  absolute  temperature,  T,  in  Centi- 
grade degrees,  and  any  pressure,  p,  in  atmospheres : 

i;  =  the  specific  volume,  metric  system. 
pv  =  BT-CpK 


OF  THE  STEAM-ENGINE.  201 

B  and  C  are  constants : 

^  =  0.0049287;,        C=  0.187815. 

This  empirical  formula  seems  to  hold  equally  good  for  the 
specific  volume  of  both  saturated  and  superheated  steam, 
giving  very  close  results  in  either  case. 

Therefore,  denoting  by  V^  and  T^  the  specific  volume  and 
absolute  temperature  of  superheated  steam  of  a  pressure  p, 
we  have 


(226) 


If  we  transform  this  formula  for  the  ratio  of  the  specific 
volumes  into  Fahrenheit  degrees  and  pounds  pressure  (ab- 
solute) per  square  inch,  we  have 

^^^^T.^459.4-35.022V-g  ^226a) 

7^+459.4-35.0221/^6 

In  this  formula,  S^,  is  the  specific  volume  of  superheated 
steam  at  the  pressure  Pj,  and  T^  is  the  temperature  of  the 
superheated  steam  in  degrees  Fahrenheit. 

Tg  can  be  obtained  by  direct  measurement  of  the  tem- 
perature in  the  steam-pipe,  or  can  be  deduced  with  sufficient 
accuracy  by  multiplying  its  excess  of  thermal  units  over 
saturated  steam  by  2,  and  adding  this  to  the  temperature 
of  saturated  steam. 

We  have  mentioned  the  extreme  avidity  of  the  absorp- 
tion and  emission  of  the  heat  of  the  steam  by  the  interior 
surface  of  the  cylinder.  We  should  also  recollect  that 
strong  currents,  swirls,  and  eddies  exist  in  the  steam  as  it 
enters.  Hirn  assures  us  that  it  is  possible  for  the  steam  not 
in  contact  with  the  iron  walls  to  remain  superheated,  and 


202  THE  RELATIVE  PROPORTIONS 

this  may  be  true  wholly  or  only  in  part.  We  believe  it  to  he 
saturated  steam. 

Equation  (220  h),  if  we  take  G  in  British  units  and  mul- 
tiply it  by  2,  under  the  assumption  that  the  specific  heat  of 
steam  is  0.5,  will  give  the  degrees  of  superheat  required,  so 
that  the  heat  abstracted  by  the  iron  may  be  met,  and  the 
case  be  equivalent  to  the  use  of  saturated  steam  in  an  adia- 
batic  cylinder,  without  this  preliminary  loss  of  heat. 

There  is  a  preliminary  condensation  and  a  mass  of  more 
or  less  superheated  steam  inside  at  the  point  of  cut-off. 
There  must  be  a  more  rapid  re-evaporation  during  expan- 
sion, and  a  less  amount  of  water  for  re-evaporation  during 
exhaust.  It  is  currently  believed  that  superheating  tends 
to  score  the  cylinder,  by  causing  such  thorough  re-evapora- 
tion during  exhaust  as  to  leave  the  cylinder  dry  and  hot. 
Hirn  fixes  the  safe  temperature  of  superheated  steam  at 
446°  Fahr.  It  is  easy  to  see,  however,  from  equation 
(220  6),  that  diflfering  proportions,  pressures,  and  speeds 
require  different  amounts  of  superheat. 

Hirn,  since  1850,  has  devoted  his  talents  as  an  experi- 
menter and  his  profound  knowledge  of  practical  thermo- 
dynamics to  experimental  verification  of  thermodynamic 
laws. 

The  following  resume  of  his  results  is  taken  from  the  work 
of  M.  Marcel  Deprez  {Eev.  Univ.  des  Mines ,  1874)  : 

(1)  "  A  compound  Woolf  engine,  worked  for  fifteen  years 
with  saturated  steam,  consumed  12^  kilogrammes  of  steam 
per  horse-power  per  hour  (French).  Suppressing  the  first 
cylinder  and  working  with  superheated  steam  expanded 
four  times,  the  steam-consumption  fell  to  10  kilogrammes. 

(2)  "In  another  engine  without  jacket,  with  a  single 
cylinder  and  4  expansions,  the  consumption  was  14.T5  kilo- 
grammes with  saturated  steam,  and  fell  to  10  kilogrammes 
with  the  steam  superheated  to  250°  Centigrade. 


OF  THE  STEAM-ENQINE.  203 

(3)  "  The  two  cylinders  of  the  Woolf  engine  having  been 
replaced  by  a  single  cylinder  without  jacket,  the  pressure 
being  4^  atmospheres,  arid  with  4  expansions,  the  consump- 
tion fell  to  8.53  kilogrammes. 

(4)  "  In  a  high-speed  engine  (93  revolutions  per  minute), 
pressure  3|  atmospheres,  4  expansions,  steam  superheated 
to  250°  Centigrade,  the  consumption  fell  to  8.2  kilogrammes 
per  horse- power  per  hour. 

(5)  "  In  an  engine,  pressure  5  atmospheres,  6  expansions, 
superheated  to  245°  Centigrade,  the  consumption  was  7|- 
kilogrammes  per  horse-power  per  hour. 

"  In  Number  4,  the  throttle  being  almost  closed  and  th^ 
expansion  very  little,  the  consumption  was  9.2  kilogrammes. 
Number  5,  under  the  same  conditions,  consumed  10  kilo- 
grammes. 

"All  these  results  were  obtained  for  long  periods;  the 
power  was  measured  by  a  brake ;  all  were  condensing  en- 
gines, the  last  three  having  four  valves ;  all  were  without 
steam-jackets,  because  M.  Hirn  believed  superheating  ren- 
dered them  useless." 

We  see  that  M.  Hirn  attained  by  these  expedients  a 
greater  economy,  with  very  moderate  pressures  and  expan- 
sions, than  is  usual  in  practice,  by  preventing  transmission 
of  heat  through  the  cylinder-walls  and  by  preventing  initial 
condensation. 

Hirn  declares  that  improvement  rendering  the  use  of 
superheated  steam  safe  and  practicable  is  the  greatest  pos 
sible  advance  in  steam-engine  economy. 

We  cannot  agree  with  Hirn  that  steam-jackets  are  useless 
in  all  cases, — they  are  at  times  and  in  some  places  necessary 
to  the  highest  economy, — or  that  proper  compounding  is  not 
beneficial. 

The  proof  in  two  cases  that  throttling  does  not  seriously 
affect  the  consumption — which  was  probably  increased  by 


204  THE  RELATIVE  PROPORTIONS 

the  absence  of  expansion  only,  and  prevented  from  becoming 
very  great  by  the  reduced  initial  pressure  and  temperature 
of  the  entering  steam — is  of  very  great  value  as  affecting 
the  relative  economy  of  automatic  cut-off  and  plain  slide- 
valve  engines  with  a  throttling  governor.  Indeed,  there  is 
very  little  doubt  that,  in  the  case  of  small  cylinders,  quite 
as  great  economy,  if  not  a  greater,  is  as  often  attained  with 
the  throttling  governor  as  with  an  automatic  cut-off. 

(79.)  The  Influence  of  the  Steam- Jacket.— The  steam- 
jacket  should  surround  the  whole  of  the  cylinder  at  sides 
and  ends.  Except  by  means  easily  deranged,  it  seems 
hardly  possible  to  introduce  steam  into  the  piston-head. 

There  is  a  steady  progress  of  heat  from  the  jacket  to  the 
interior  surface  of  the  cylinder,  having  the  effect  of  dimin- 
ishing the  initial  condensation,  facilitating  the  re-evapora- 
tion during  expansion,  and  increasing  the  amount  of  heat 
lost  through  the  exhaust-port. 

Diminishing  the  amount  of  water  condensed  is  the  surest 
means  of  preventing  loss  by  re-evaporation  during  exhaust. 

Compared  with  very  bad  engines,  the  extraordinary  pre- 
cautions taken  in  adding  and  covering  a  jacket  quite  fre- 
quently produce  a  great  saving  of  steam ;  but  it  is  very 
doubtful  if  any  very  great  gain  is  made  in  the  case  of  well- 
covered  engines. 

Well-authenticated  cases  of  a  saving  of  3  to  5  per  cent, 
are  cited ;  but  that  error  is  more  than  probable  in  the  use 
of  indicators  during  a  test,  and  may  have  occurred. 

The  sum  total  of  this  action  of  the  jacket  would  seem 
favorable  to  economy,  as,  w^ith  a  dry  cylinder,  the  steam  in 
the  jacket  can  lose  only  by  radiation,  a  comparatively  slow 
process. 

(80.)  The  Influence  of  the  Valve -Movement. — 
Where  the  plain  Z)-valve  with  three  ports  is  used,  conden- 
sation occurs  in  the  steam-chest,  the  exhaust  steam  passing 


OF  THE  STEAM-ENOINE.  205 

through  the  hollow,  taking  heat  from  it,  which,  in  turn, 
is  supplied  from  the  "  live"  steam  in  the  steam-chest. 

Single  slide-valves  for  two-cylinder  engines  prove  fre- 
quently to  be  the  cause  of  large  losses  which  are  unsus- 
pected. 

It  would  seem  to  be  a  pretty  well  established  fact  that, 
wherever  steam  economy  is  the  first  consideration,  four- 
ported  cylinders  should  be  used,  and  every  possible  means 
to  prevent  iron  surfaces  from  being  alternately  exposed  to 
higher  and  lower  temperatures  of  steam. 

The  advantage  resulting  from  compression,  superheating, 
steam-jacketing,  and  compounding  steam-cylinders  will  be 
much  more  apparent  in  small  than  in  large  cylinders ;  be- 
cause in  small  cylinders  we  have  a  larger  proportion  of 
iron  surface  to  the  volume  of  steam  used  per  stroke  and 
per  minute. 

We  will  refer  more  at  length  to  compounding  of  steam- 
cylinders,  after  having  determined  the  value  of  C  in  a 
number  of  cases. 

(81.)  Computation  of  Condensation. — Bearing  in 
mind  these  many  qualifying  conditions  surrounding  the  ac- 
tual use  of  steam  in  the  engine,  let  us  take  up  and  compare 
the  condensation  in  the  case  of  several  different  engines. 
(Table,  page  206.) 

The  experiments  of  J.  W.  Hill  were  made  to  decide  the 
relative  economy  of  three  types  of  engines,  built  by  rival 
makers,  and  were  published  in  pamphlet  form,  after  the 
tests,  without  award,  as  the  results  were  very  close. 

The  experiments  of  Messrs.  Gately  and  Kletzsch  were 
made  with  a  view  to  determining  the  condensation  of  steam- 
cylinders.  Their  general  course  was  directed  by  Professor 
Thurston,  to  whom  the  writer  had  previously  communicated 
his  views  and  published  writings  on  initial  condensation  in 
steam-cylinders. 

18 


206 


THE  BELATIVE  PROPORTIONS 


'9  JO  eni^A  . 

Snjpaoaad  uiojj  j;  jo  onx^A. 


•jg[o-:tno  ye  anon  J»(I  "d'H         b:. 


S  S5  -0 

W  O  H 

3  a 


•»B9H 

JO  sjtna  qsi^ua  ai 


•lUB9Jg  JO  'sqi  ui    ^ 


•jgo-»no  %v  ui'Ba^g 
pa;«oipai  o:^  i«npv  JO  op^a; 


pai^Baqjadng  jo  aoinxoA^  ogpadg 


•jtfo-;no  YB  uiBajg 
pa^BJu^Bg  JO  9uin[OA.  ogpadg 


•"'or  joj  m^ajg 
pajBaqjadng  jo  ajnijujadniax 


•(•jqBj)  Saijuaq 
-jadng  JO  saaaSaQ  jo  aaqranit 


•;snBqxa 
joj  japuiijfQ  JO  ajn^BJodniax 


•uoissa.idraoo  ianuiix'8i\[ 
JOJ  jopai[jfo  JO  ajnjuaaduiax 


^■8  .iapaiiA'3  JO  aanj^aoduiax 


•qouj  aj^abg  jad 
spatioj  '83ioa;g-pii\[  ^18  jsnuq 
-xg  JO  aanssajti-uiBajg  ejniosqy 


•qoui  ajBnbg  aad  spaiioj  'aan 
-ssajd  uoissajduioo  ranuiixBi\[ 


•j^o-:jn3  ye  q^ai  eJBubg  jad 
epunoj  ui  ejnssejj  9;n[osqy 


•(sjtufi 
qsi;tja)  pasn  uiuajg  jo  jf:mBn5 


•9;natj\[  jad  sajtojjg  jo  jaqninx    !?; 


•snoTSu'Bdxa 
JO  jtaqrati]^  anjx  Jo  iBoojdpa^ 


'%99S.  ni  japnjiiCQ  JO  ja:jauiBi(i    •« 


•aotiBaBaio  enid 
^aa^  ni  japuji^CQ  jo  aJio.ng 


•^narauadxa  jo  ^OI:^B.ln(I 


■;nani 
-padxa  JO  jaqninii  eonajajag 


X 


oo 

128 

CO  oo 


'Se660"0  'aSBaaAY 


f*"     oo  t- 


3  8 

cot-- 
id  id 


w  if 


CO  ^ 
CO  lO 


o 


odd 


si 
O 

o 
n 


B 

r^:::J 

•b^ 

f^s 

^ 

^?^ 

MM 

•3 

E^!g 

^S 

88  is  Is 

d  c>  da  d  OS 


OF  THE  STEAM-ENQINE. 


207 


•raBa^g  jo  'sqi  ui    ^ 


•J50-}no  VB  uiBajg 
pajBoipai  o}   [uujov  jo  ojiuji 


•j[)o-4no  va  ni«9}g  ^ 

pajTiaqjadng  jo  oran[OA.  ogpadg    ^ 


•ifojno  }tj  tmjejg 
pn^BjnjBg  JO  erauiOj^  ogpadg 


pa^'eaqjadng  jo  9jn:>ui8dm»x    ^ 


-jadng  JO  saaaSod  jo  aaqmnx 


•isntjqxa; 
joj  japaji^o  JO  9.m?njadui9x 


•uoissajdraoQ  ninunxBK 
JOJ  jspujiiCj  JO  ojiUBjadraox 


■ye  JoputiA'3  jo  ajnjBjadniox 


•qouj  a.iTJtibg  jad 
spano,!  *aj[0Jig-pip{  jb  jsnuq 
-xa  JO  ajnssaa<j-iuBa}g  ajniosqy 


•qoai  ajBnbg  aad  spanoj  'ajn 
-ssajd  uoissaadraoo  ranraiXBK 


•jjo-jno  ys  qoni  ajBnbg  jad 
spunoj  ai  aanssajj  a^njosqv 


•(ffHUQ 

qsijua)  pasn  rana^g  jo  .(jixBn^ 


a^nuiK  J9d  eaiiojjg  jo  jaqran^f    fe; 


•saoisamlx^ 
JO  jaqransj  aii.ix  Jo  iBOoadioaa 


•jaa^  ni  japuji^to  jo  ja^araBio:    -e 


•:jaaj  ui  japajiiCo  jo  e^ojjg 


•;aarauadxa  jo  nonBanQ     S 


•jiiara 
-uadxg  JO  jaqmnjj  oonajajaji 


•"•cooo    ocooo    cooo    oco 
^  d  o  d  d_d _o_d_o'  d_d  a  d,  d^    d  d  d 

>> 

-o 

Ci     : 
a!     :    : 


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r-l  ?0  Cl     (M  r-l  I 


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r-li-H-l.-l  rir-'  i-Hr-irH  (M(N(NO?  i-ir-rH 


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1-100  00      O  CD  O  t- <M 

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95  S  55  tt    rr'  05 


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**  Si2*^'~'    00  CO  T*  o  i^    <M  Ci-i  CO    00  —  T-i  "o        ST" 

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^_  S     d_ 

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i-i 

i^Q0^O~  J^oTm^S"   COt^^oT  S~^-^  to" 

(MIMIM  (N 


208  THE  RELATIVE  PROPORTIONS 

The  experiments  of  tlie  International  Electrical  Exhibi- 
tion of  1884  were  conducted,  under  a  code  drawn  up  by  the 
writer  and  approved  and  adopted  by  the  Franklin  Institute, 
by  H.  W.  Spangler,  Assistant-Engineer,  U.S.N. 

In  the  cases  in  the  preceding  table  the  piston  was  known 
to  be  tight  and  a  trifling  leakage  to  occur  at  the  valves. 

Unless  the  piston  and  valves  are  proved  to  be  tight,  experi- 
ments upon  steam-engines  have  no  scientifie  value. 

For  this  reason  these  results  have  not  that  absolute  accu- 
racy so  desirable  in  all  scientific  work ;  but  they  represent 
the  best  results  attained  by  our  mechanics  skilled  in  engine- 
building,  and  for  that  reason  may  be  of  greater  practical 
value  than  results  derived  from  more  accurate  work  under 
conditions  not  realizable  in  practice. 

(82.)  Probable  Errors  of  the  Table  (pages  206,  207). 
— In  Mr.  Hill's  experiments,  his  extreme  care  in  computa- 
tion renders  the  possibility  of  error  in  the  value  of  the  con- 
stant of  condensation  very  slight.  The  difference  observable 
in  each  engine,  condensing  and  non-condensing,  is  due  to  the 
slight  leakage  at  the  valves,  to  the  probable  errors  of  the 
indicators  used,  and  to  the  practical  impossibility  of  closely 
measuring  the  exact  points  and  pressures  on  the  indicator 
diagrams,  as  well  as  to  the  short  time  of  exposure  to  com- 
pression temperatures. 

Mr.  Hill  writes  as  follows : 

"  Cincinnati,  February  2,  1884. 

"  Dear  Sir, — The  calorimeter  used  in  the  tests  for  quality 
of  steam  at  the  Miller's  Exhibition  was  of  the  continuous 
kind,  carefully  made,  and  in  charge  of  my  principal  assist- 
ant. 

"  I  accepted  his  notes  and  data  as  correct  at  the  time,  but 
from  more  recent  experiments  am  inclined  to  doubt  any  re- 
sult from  a  calorimeter  of  this  kind,  owing  to  the  fact  of 
large  variations  in  the  temperature  of  overflow  (known  to 


OF  THE  STEAM-ENGINE.  209    ^^ 

subsist  by  other  circumstances)  not  recorded  by  the  ordinary 
mercurial  thermometer.  f^j 

"  I  now  use  a  simple  arrangement  of  tub,  scale,  and  hand  .^^ 
thermometer,  and,  while  this  method  is  liable  to  error,  the 
error  is  not  sufficient  to  lead  you  astray. 

"  For  the  purpose  of  comparison  I  regard  the  calorimeter 
data  of  the  Miller's  Exhibition  trials  as  correct,  but  cannot 
endorse  it  for  absolute  results. 

"  I  know  the  Harris  piston  was  tight,  from  special  test. 

"Page  74.  There  is  no  doubt  all  the  engines  suffered 
from  leaks  into  and  out  of  cylinder  through  steam-  and 
exhaust-valves." 


There  is  no  doubt  in  the  mind  of  the  writer  that  super- 
heated steam  did  not  reach  these  engines.  It  would  appear 
from  the  results  attained  that  all  of  the  engines  were  tight 
as  to  pistons.  Messrs.  Gately  and  Kletzsch  state  that  the 
engine  upon  which  they  experimented  was  tight  in  valves 
and  piston. 

When  compression  is  neglected,  as  is  done  for  the  pur- 
pose of  comparing  Mr.  Hill's  work  with  that  of  Messrs. 
Gately  and  Kletzsch,  it  will  be  seen  that  the  variation  from 
the  mean  value  of  C=. 01814  pound  of  steam  is  remarkably 
small.  It  would  seem  probable,  however,  that  the  true  value 
of  C  is  greater  than  16.045  British  units,  which,  however, 
will  prove  the  most  useful  constant  for  general  work  in 
which  compression  is  not  closely  regarded. 

Especially  where  the  clearance  is  very  small  the  exhaust 
closure  is  very  late,  and  the  time  of  exposure  of  the  piston- 
and  cylinder-heads  so  very  short  as  would  probably  prevent 
the  temperature  due  to  compression  from  acting  with  its 
full  effect.     (See  expression  given.)    We  should  neglect  the 


210  THE  RELATIVE  PROPORTIONS 

temperatures  due  to  compression,  but  not  the  steam  saved 
by  it. 

The  experiments  on  the  condensing  engines  1,  3,  and  5 
will  probably  give  the  most  accurate  values  of  C.  All  of 
these  engines  were  built  by  our  best  makers  for  the  special 
purpose  of  a  competitive  test,  and,  most  fortunately,  the 
elaborate  record  of  them  was  made  by  a  thorough  and 
experienced  engineer. 

The  experiments  of  Messrs.  Gately  and  Kletzsch,  al- 
though marked  by  less  care  and  precision,  supplement  Mr. 
Hill's  work,  by  enabling  us  to  prove  the  law  of  condensa- 
tion to  be  true  under  all  conditions  as  to  speed,  initial  ex- 
haust, and  back  pressures  and  points  of  cut-off.  Their  short 
duration  gives  them  less  value  and  renders  them  less  relia- 
ble as  to  absolute  results.  The  clearance  should  have  been 
experimentally  determined.  Diagrams  should  have  been 
published  in  conjunction  with  the  record,  and  the  amount 
of  compression  carefully  noted,  as  it  doubtless  has  an  im- 
portant effect  upon  the  initial  condensation  of  steam. 

These  concordant  experiments  were  made  with  pressures 
varying  from  102  to  27  pounds  at  cut-off,  with  speeds  varying 
from  152  to  67  strokes  per  minute,  with  the  true  cut-off  vary- 
ing from  .131  to  .981  of  the  stroke,  with  and  without  con- 
denser, and  by  different  experimenters  upon  different  engines. 

The  condensation  for  the  Buckeye  engine  is  roughly  com- 
puted to  show  the  injurious  effect  of  a  slide-valve  bathed  in 
exhaust-steam.  Although  this  engine  was  not  tested  for 
tightness,  the  deservedly  high  reputation  of  its  makers 
would  render  improbable  any  serious  loss  by  leakage. 

(83.)  The  Influence  of  the  Condenser.— The  con- 
denser adds  about  10  pounds  to  the  mean  effective  pressure 
upon  the  piston ;  it  cools  the  exhaust  about  60°  Fahrenheit  ; 
it  demands  power  for  pumping ;  and  it  may,  when  the  en- 
gine is  too  lightly  loaded,  increase  the  actual  consumption 


OF  THE  STEAM-ENOINE.  211 

of  steam  per  horse-power  per  hour.  The  sudden  increase 
in  the  fall  of  temperature  of  steam  in  the  last  three  or  four 
pounds  of  pressure  above  a  vacuum  has  taught  makers,  by- 
practical  results,  not  to  carry  their  vacuums  too  far  down. 

From  the  indicator-card  can  be  calculated  the  amount 
of  steam  from  the  boiler  required  to  do  the  work  and  meet 
the  demands  of  condensation.    Equations  (219)  and  (223  a.) 

(8-1:.)  The  Jet- Condenser. —The  jet-condenser  is  the 
cheapest  and  most  ejfficient,  and  should  be  used  whenever 
the  quality  of  the  Water  will  permit. 

Whatever  temperature  for  the  mixture  of  condensing 
water  and  steam  is  required  will  give  the  weight  of  con- 
densing water  from  the  following  equation : 

in  which 

Wa  =  actual  steam  per  indicated  HP  per  hour  in  pounds. 
Ha  =  British  units  of  heat  in  one  pound  of  steam  at  boiler. 
We  =  condensing  water  in  pounds  per  hour  per  HP, 
He  =  its  heat  units  per  pound. 

T^    =  the  approximate  temperature  of  water  flowing  from 
the  condenser  (Fahr.). 

(85.)  The  Surface-Condenser. — The  surface-condenser 
should  only  be  used  when  it  is  necessary  to  separate  the  con- 
densing water  from  the  boiler  feed-water,  and,  as  a  matter 
of  convenience,  it  should  have  separate  circulating  and  ex- 
haust-pumps. In  most  cases,  although  it  is  a  proceeding  less 
economical  of  coal,  it  will  be  found  to  have  many  advan- 
tages. It  is  usual  among  designers  to  allow  from  tw^o  to  four 
square  feet  of  condensing  surface  per  indicated  horse-power. 

Isherwood  states  (Shock's  Steam-Boilers,  page  38)  that 
the  conductivity  of  metal  plates  is  independent  of  their 
thickness,  and  that  for  a  difference  of  temperature  of  one 


212  THE  RELATIVE  PROPORTIONS 

degree  Fahrenheit  one  square  foot  will  transmit  the  following 
numbers  of  heat  units  per  hour  : 

Copper 642.543  British  units. 

Brass 556.832 

Wrought  iron 373.625 

Cast  iron 315.741 

It  is  not  safe  to  reckon  more  than  10  to  20  per  cent,  of 
the  above  values  in  actual  condensers.  The  steam  carries 
with  it  the  cylinder  lubricants,  which  foul  the  surfaces  of 
the  tubes,  and  the  condensed  steam  collects  on  the  tubes, 
preventing  their  rapid  action,  while  the  high  vacuum  may 
materially  degrade  the  efficiency  of  the  condensing  sur- 
faces. 

The  steam  released  from  the  cylinder  at  the  terminal 
pressure  of  expansion  still  further  expands  into  a  body  of 
steam  in  the  condenser,  and  then  condenses. 

The  circulating  condensing  water  rises  in  temperature 
from  20°  to  40"^  Fahr.  The  larger  the  condensing  surface 
per  indicated  horse-power,  the  higher  the  allowable  rise  of 
temperature.  To  be  on  the  safe  side,  the  estimated  trans- 
missive  power  of  the  condensing  surfaces  should  not  exceed 
20  per  cent,  or  less  of  Isherwood's  values,  and  the  temper- 
ature of  the  steam  in  the  condenser  should  be  estimated 
from  the  vacuum-pressure. 

Let  Cj  =  constant  of  transmission. 
"     T„  -=  temperature  of  vacuum. 
"     Tk  =  mean  temperature  of  circulating  water. 
"  Ha  =  total  heat  of  steam  at  boiler. 
"     A  =  condensing  surface. 

Then 

10  to  20%  of  C,{T,-T,) 


OF  THE  STEAM-ENGINE.  213 

Let  21  =  ^^1^. 

"  Tj  =  temperature  of  entering  circulating  water. 

"  T^  =  temperature  of  departing  circulating  water. 

"  We  =  weight  of  circulating  water  in  pounds. 

"  T^  =  heat  units  of  condensed  water. 

Then  we  have 

"  T —  T  "* 

Both  of  these  formulae  are  approximations,  giving  suffi- 
ciently close  values  for  an  estimate  of  cost  of  making  and 
of  power  required  by  pumps.  Much  more  frequently  than 
is  believed,  additional  expense  for  power  is  the  result  of 
adding  a  condenser. 

(86.)  The  Law  of  Re -evaporation  after  Cut-off.— 
"Whenever  we  examine  the  indicator-cards  correctly  taken 
from  engines  with  practically  tight  valves  and  piston,  not 
embarrassed  by  sluggish  valve-motions,  we  find  the  curve 
of  expansion  to  follow  very  closely  the  equilateral  hyper- 
bola. We  also  find  that  the  quantity  of  steam  present  as 
vapor  is  a  minimum  at  the  point  of  cut-off,  and  that  it 
steadily  increases  in  volume  as  the  expansion  goes  on, 
reaching  a  maximum  at  the  point  of  release. 

The  added  steam  appearing  at  the  point  of  release  should 
come  from  the  condensation  at  the  cut-off,  which  condensa- 
tion should  be  decreased  in  conformity  with  the  law  of  con- 
densation already  stated. 

Let  3y  =  temperature  of  pressure  at  release. 
"   Y^  =  value  of  curve  of  condensation  for  e^  (at  release). 

"We  can  then  write  from  equation  (221), 

Condensation  at  cut-off  _  (^6  -  ^e)  {d  +  Ys) 
Condensation  at  release     {Tf—Tt){d-\-  Yh') 

Mr.  Hill  computed  the  steam  from  his  diagrams  at  the 


214 


THE  RELATIVE  PROPORTIONS 


point  of  release,  the  writer  for  the  point  of  cut-off  from  the 
same  diagrams. 

A  comparison  will  afford  additional  verification  of  the 
law  of  condensation,  and  show  the  law  of  re-evaporation  to 
be  identical.  Writing  this  in  its  most  complete  form,  we 
have 

The  following  table  gives  the  results  computed  by  this 
formula,  and  also  the  results  of  Mr.  Hill's  independent 
calculations  and  measurement : 


's 

2 

Sa'  *.S 

'it'Milii 

g 

ll 

02     . 

2  " 

M    S 

0  2 
^1 

Si- 
ll 

^1 

Si 

=2 

Si's 
*  s 
c  .2 

<2 

1 

IS 
> 

II 

11 

It 

el 

I'l 

^f 

^/ 

w\ 

r\ 

rl-1 

1 

0.94 

.967 

14.57 

211.8 

13.755 

1.408 

-A 

2 

0.97 

.983 

17.04 

219.5 

18.013 

1.327 

n 

3 

0.96 

.978 

14.04 

209.6 

13.915 

1.400 

-28 

3^ 

4 

0.97 

.983 

17.46 

220.8 

19.674 

1.267 

i  to 

From  Precedingr  Table. 

5 

0.98 

.989 

15.16 

213.6 

14.886 

1.385 

1 

6 

0.98 

.989 

17.41 

220.6 

18.896 

1.373 

III 

r— 1 

n-2'c 

^/-^e 

n-2'e 

F 

1,  3,  and  5 

averages 
2, 4,  and  6 

978 

14  44 

211  6 

1  395 

355 

581 

93 

57  4 

172 

Ml 

averages 

.985 



220.3 

1.323 

.238 

.459 

40.6 

6.3 

114.7    .361 

The  calculated  value  falls  short  of  the  observed  value  by 
4  per  cent.,  or  about  \  pound  of  condensation  per  horse- 
power per  hour  for  the  engines  with  condenser.  For  the 
engines  non- condensing  the  calculated  value  falls  short  8 
per  cent,  of  the  indicated  steam  per  horse-power  per  hour, 
or  about  li  pounds. 


OF  THE  STEAM-ENGINE.  215 

A  certain  amount  of  this  condensation  is  due  to  heat 
converted  into  work.  This  difference  is  in  the  expected 
direction,  for  the  engines  were  none  of  them  steam-jacketed, 
and,  being  subject  to  loss  from  radiation,  some  additional 
lack  would  naturally  be  anticipated.  The  undoubted  leaks 
into  and  out  of  valves  would  appear  to  affect  the  diagrams 
of  the  engines  non-condensing  most  seriously. 

It  would  also  appear  that  the  intensity  of  the  pressure  of 
the  compressed  steam  facilitated  its  condensation,  otherwise 
the  results  calculated  with  compression  would  not  agree 
better  with  the  facts  than  when  calculated  without  compres- 
sion, as  can  be  seen  by  trial. 

It  is  of  particular  importance  to  show  the  practical  iden- 
tity of  the  laws  of  condensation  and  re-evaporation  as  a 
preliminary  to  the  discussion  of  compounded  cylinders. 

(87.)  The  Influence  of  Compounding  Cylinders.— 
We  have  carefully  followed  the  action  of  the  steam  while 
passing  through  one  cylinder.  Let  us  follow  it  through  the 
two  cylinders.  The  steam  entering  the  non-condensing  cyl- 
inder suffers  initial  condensation,  in  some  instances  quite 
copious,  but  not  so  great  as  if  the  non-condensing  cylinder 
had  the  temperature  of  the  exhaust,  T«. 

The  steam  being  cut  off  in  the  non-condensing  cylinder, 
re-evaporation  begins,  the  expansion-line  being  held  closely 
to  an  equilateral  hyperbola. 

This  re-evaporation  is,  however,  far  from  being  complete, 
and  at  the  end  of  the  stroke  communication  is  opened  to 
the  condensing  cylinder.  At  this  instant  a  relatively  enor- 
mous initial  condensation  occurs,  because  of  the  great  surface 
of  condensing  piston-  and  cylinder-head  presented  at  the 
temperature  of  exhaust ;  but  this  condensation  is  met  at 
once  by  the  equally  active  re-evaporation  which  simulta- 
neously occurs  from  the  whole  interior  of  the  non-con- 
densing cylinder,  the  result  being  the  transferring  of  the 


216  THE  RELATIVE  PROPORTIONS 

condensation  from  the  surface  of  the  non-condensing  cyl- 
inder to  the  surface  of  the  condensing  cylinder  until  the 
temperatures  are  equalized. 

After  the  violence  of  this  first  transfer  of  condensation 
has  abated,  the  re-evaporation  from  the  interior  of  both 
cylinders  occurs  with  sufficient  celerity  to  hold  the  expan- 
sion-curve closely  to  an  equilateral  hyperbola. 

If  but  twa  cylinders  are  used,  the  condensing  cylinder  is 
now  opened  to  exhaust,  and  the  re-evaporated  and  vapor- 
ous steam  enter  the  condenser,  carrying  much  more  heat 
than  would  appear  from  a  calculation  of  the  thermal 
value  of  the  vaporous  steam  present  at  the  end  of  expan- 
sion. 

Thus  we  see  that  at  the  present  day  the  compound  engine 
owes  its  possible  greater  efficiency  to  the  physical  attributes 
of  iron  rather  than  to  the  properties  of  steam,  and  that 
with  the  use  of  non-conducting  materials  the  necessity  of 
compounding  cylinders  will  vanish. 

When  cranks  of  compounded  cylinders  are  placed  at 
right  angles,  and  the  steam  is  cut  off  from  the  condensing 
cylinder  at  an  early  point  in  the  stroke,  certainly  earlier 
than  one-half  stroke,  it  will  be  found  that  a  considerable 
increase  in  the  economy  will  occur  with  a  small  receiver, 
although  this  arrangement  will  cause  trouble  in  equalizing 
the  power  of  the  cylinders,  because  of  the  increase  of  back 
pressure  in  the  non-condensing  cylinder  until  its  piston 
reaches  mid-stroke. 

This  economy  arises  from  the  fact  that  the  transferrence 
of  condensation  from  the  non-condensing  cylinder  to  the 
condensing  cylinder  is  greatly  facilitated  by  an  increased 
difference  in  temperatures  of  the  non-condensing  cylinder 
and  receiver  and  of  the  condensing  cylinder. 

The  particularly  injurious  effect  of  a  double  admission  of 
steam  to  the  condensing  cylinder  when  cranks  are  at  right 


OF  THE  STEAM-ENGINE.  217 

angles  and  the  cut-off  of  the  condensing  cylinder  is  later 
than  one-half  stroke,  arises  from  the  fact  that  this  re-evap- 
oration from  the  iron  surfaces  is  temporarily  stopped  by  the 
entrance  of  steam  of  a  higher  pressure  and  temperature 
from  the  non-condensing  cylinder. 

The  advantage  of  the  compound  engine  must  lie  in  its 
lesser  condensation  alone,  other  things  being  equal ;  and  this 
diminution  of  condensation  must  compensate  for  the  in- 
creased quantity  of  machinery  demanded  before  we  begin 
to  consider  its  superiority. 

This  point  must  be  considered  experimentally  by  a  careful 
determination  of  the  ratio  of  the  actual  to  the  indicated 
eteam  and  heat. 

For  the  purpose  of  gaining  a  clear,  general  idea,  let  us 
assume  a  perfect  gas,  expanding  according  to  Mariotte's 
law,  fed  to  a  pair  of  compounded  Cylinders  at  a  given  initial 
pressure,  Pj,  and  exhausted  against  a  back  pressure,  B,  out- 
side of  the  cylinder.  While  these  assumptions  will  not 
perfectly  fulfil  the  conditions  of  steam,  the  results  obtained 
will  serve  as  a  guide  in  the  use  of  steam,  and  by  proper 
modifications  can  be  applied  to  the  steam-engine  itself. 
AVhen  steam  is  used,  the  high  initial  temperature  of  the 
steam  is  communicated  to  the  walls  previously  at  or  above 
the  temperature  of  exhaust  by  means  of  the  condensation 
of  the  steam  which  results  in  the  water  ready  for  re-evap- 
oration at  the  instant  of  any  diminution  of  pressure.  That 
part  of  the  cylinder- walls  subjected  to  initial  steam  being 
hotter  than  the  expanded  steam  gives  the  steam  this  heat 
very  readily,  which  goes  for  the  twofold  purpose  of  recre- 
ating steam  and  of  warming  up  to  the  temperature  of  the 
steam  the  gradually  uncovered  walls  of  the  cylinders,  which 
are  at  the  temperature  of  the  exhaust  or  perhaps  above  it. 

These  exchanges  go  on  with  a  celerity  n(  t  easily  appre- 
hended without  thoughtful  consideration  of  the  great  weight 


218 


THE  RELATIVE  PROPORTIONS 


of  iron  in  the  steam-cylinder,  and  its  conductivity  for  heat 
as  compared  wi  h  the  relatively  exceedingly  small  weight 
of  steam  and  water  at  the  temperature  of  evaporation,  which 
enter  and  leave  the  cylinder  at  each  stroke. 

Theories  to  the  contrary  notwithstanding,  it  would  seem 
as  if  within  the  limits  of  economic  expansion  an  equilateral 
hyperbola  represents,  with  quite  as  great  approximation  as 
any  other  curve,  the  pressures  of  expanding  steam  in  an 
iron  cylinder  steam-jacketed  or  clothed. 

Fig.  40. 


A^ 


z 


Taking,  then,  a  perfect  gas  as  our  starting-point,  and  as- 
suming as  the  simplest  case  two  cylinders  with  cranks  180 
degrees  apart. 

Let  Yn  =  the  true  volume  of  the  non -condensing  cylinder  (in- 
cluding one  of  its  clearances,  Ic)  up  to  its  valve-face. 
Yr  =  the  volume  of  the  connecting  channels  (and  receiver, 

if  there  is  one)  from  valve-face  to  valve-face. 
Fc  =  the  true  volume  of  the  condensing  cylinder  (includ- 
ing one  of  its  clearances,  h^  up  to  its  valve-face, 
e  =  the  true  cut-off  of  the  non-condensing  cylinder  =  the 
reciprocal  of  the  true  expansion  in  it. 
Pft  =  the  initial  pressure  of  the  non-condensing  cylinder, 

pounds  per  square  inch  abs. 
ej=the  true  cut-off  of  the  condensing  cylinder  =  the 

reciprocal  of  the  expansion  in  it  after  cut-off. 
J5-=the   back   pressure   of   the   condensing   cylinder, 
pounds  per  square  inch  abs. 

19 


OF  THE  STEAM-ENGINE.  219 

After  a  compound  engine  has  attained  its  regular  work, 
it  has  attained  such  a  pressure,  P^,  in  the  receiver  (the  word 
receiver  will  be  used  to  comprise  all  pipes,  steam-chest,  etc., 
that  may  be  between  the  two  cylinders,  whether  there  be  a 
specially-designed  receiver  or  not)  as  will  enable  the  con- 
densing cylinder  to  void  the  same  weight  of  vapor  at  each 
stroke  as  is  received  by  the  non-condensing  cylinder  at  each 
stroke,  and  we  can  therefore  write  the  equation 

p_eP,V^_eP, 

The  pressure  Pr  is  that  occurring  at  the  exact  moment 
when  the  port  to  the  non-condensing  cylinder  is  closed,  and 
when  the  piston-head  of  Vc  is  at  a  distance  Cj  from  the  begin- 
ning of  its  volume.     (See  Fig.  40.) 

The  absolute  mean  pressure  pressing  forward  upon  the 
non-condensing  piston-head  can  be  written 

1" 


eP, 


1  +  nat.  log 


-P.h. 


At  the  moment  of  the  closing  of  the  steam-port  Vc  the 
pressure  P^  exists  in  all  three  divisions,  pressing  forward  in 
Vc  upon  the  piston,  pressing  backward  in  Vn  upon  the  piston. 

The  backward  pressure  upon  the  piston  of  F„  can  now  be 
calculated  at  any  point  from  the  beginning  of  stroke  to  e^. 
P,[(l-e,  +  ^)K+F.+e,FJ=P.[(l-x-f^)K+F.+xFJ. 

Therefore  the  mean  back  pressure  absolute  reduced  to  a 
full  stroke  upon  the  non-condensing  piston,  while  the  two 
pistons  proceed  in  opposite  directions  through  a  fraction  of 
the  volume  (e^  —  k),  is 

This  is  also  the  mean  forward  pressure,  absolute,  upon  the 
piston  of  the  condensing  cylinder. 


220  THE  RELATIVE  PROPORTIONS 

When,  now,  the  port  of  the  condensing  cylinder  is  closed, 
the  two  pressures  part  company,  the  back  pressure  in  the 
non-condensing  cylinder  rising  first  by  compression  into  the 
receiver  and  itself,  and  when  the  non-condensing  exhaust  is 
closed  rising  still  more  rapidly  by  compression  into  the 
clearance  of  Vn,  and  the  vapor  in  the  condensing  cylinder 
expanding  and  its  pressure  falling. 

Let  us  consider  first  the  back  pressure  in  the  non-con- 
densing cylinder,  while  the  piston  moves  through  the  frac- 
tion of  the  stroke  (l-e^).  We  can  write  the  following 
equation : 

Therefore  we  have  the  mean  absolute  back  pressure,  when 
the  non-condensing  exhaust  is  not  closed  till  the  end  of  the 
stroke. 

Secondly,  the  forward  expansion   pressure  in   the  con- 
densing cylinder,  after  its  port  to  the  receiver  is  closed. 
We  can  write  the  following  equation : 

P,[e^FJ-P^F«. 
Therefore  its  absolute  mean  pressure  is 

e^Pr  nat.  log  -• 

Finally,  if  compression  is  used  in  the  condensing  cylinder, 
the  point  at  which  compression  begins  being  the  fraction  b 
of  the  volume  of  the  condensing  cylinder,  we  have 


B 


1-b 


(l-nat.log|)^ 


We  can  now  write  the  expressions  for  the  mean  effective 
pressure  in  each  cylinder. 


OF  THE  STEAM-ENQINE. 


221 


For  the  non-condensing  cylinder  we  have,  as  the  expres- 
sion for  the  work  done  by  it  in  one  stroke, 


{-•[ 


1+nat.  log- 


p,  p,ra-«,+^)F„+F,+6,F.i 


nat.  log 


(l+^-)K  +  K+(Fe-K>,    P.[(l-6,+^0Fn+F. 
(l+^)r.+  F+(F-F.)^  F. 


nat.  log 


Vr+Vnk 


(227  a) 


The  expression  for  the  work  done  by  the  condensing  cyl- 
inder during  one  stroke  is,  if  we  assume  k  =  ki, 

^  '  c         y  n 

(l+^)F.+  F+(Fe-F.)g,  p  J  1 

l-i^(l-nat.  log-^]    |.  (227  5) 

Assume  Fr  =  0,  ^  =  0,  ^j  =  0,  B  =  0,  and  therefore  Cj  =  1 . 

Equate  equations  (227  a)  and  (227  b)  under  these  as- 
sumptions, we  have  then  the  following  criterion  in  order  to 
equalize  the  power  of  the  cylinders : 


B 


2R    _  log  2.7183^ 
E-1  log  i? 


(227  c) 


There  is  no  fall  in  pressure  from  non-condensing  to  con- 
densing cylinder  when  communication  is  opened  between 
them. 

If  we  do  not  assume  B  =  0,  we  have     • 


nat.  log  E 

19* 


2B 
E-1 


nat.  log  B 


1.^1 


222 


THE  RELATIVE  PROPORTIONS 


or,  in  common  logarithms, 


^""^'-^^r:^  i^g-^-  - 


1+E 


B 


2.3026 

Approximate  values  of  J?,  E,  and  e  under  these  conditions 
will  be  found  tabulated  below,  the  term  E—  being  neg- 
lected  as  being  very  small,  as  it  usually  is,  condensing. 

(88.)  The  Relation  of  Cylinder  Ratio  to  Ultimate 
Expansion. 

Table  of  Ratios  of  Cylinders  and  of  Points  of  Cut-off 
in  Non- Condensing  Cylinder  for  Ultimate  Expansions 
of  Steam. 

Criterion  — -— ~ —  =  log  2.7183  .Efor  equal  powers. 
ji  —  1 

E=I^+RiQV  equal  initial  thrusts. 


Batio  of 
Cylinder 
Volumes. 

UUimate 
Expansion 
of  steam. 

Point  of  Cut- 
ofif  in  Non- 
Condensing 
Cylinder. 

Remarks. 

For  Equal 
Initial 
Thrusts. 

B 

E 

-1 

E 

VA 
1% 

2 

2K 
2% 
3 
3^ 

4 

3.426 

4.190 

5.015 

5.886 

6.813 

7.801 

8.840 

9.933 

10.961 

12.277 

13.580 

14.832 

0.37 
.      0.35 
0.34 
0.34 
0.33 
0.32 
0.31 
0.30 
0.30 
0.28 
0.28 
0.27 

These  computations  are 
made  for  general  guidance 
only,  nearly  all  the  as- 
sumptions made  being  im- 
possible of  exact  realiza- 
tion. 

It  is  assumed  that  a  per- 
fect gas  is  used  expanding 
isothermally,  that  there  is 
no  back  pressure  on  the 
condensing  cylinder  pis- 
ton, and  that  there  are  no 
clearances  or  receiver,  and 
further  that  there  is  no 
cut-off  at  all  for  the  con- 
densing cj'linder,  that  onlj' 
being  demanded  to  pro- 
vide for  receivers  and  clear- 
ances in  actual  practice, 
and  that  the  cranks  are 
together,  or  180  degrees 
apart. 

2.812 

3.750 

4.812 

6.000 

7.312 

8.750 

10.312 

12.000 

13.812 

15.750 

17.812 

20.000 

OF  THE  STEAM-ENOINE.  223 

If  we  require  equal  initial  piston  thrusts  at  the  commence- 
ment of  each  stroke,  we  have 

P,-ePj,=  leP,-B^E  or  E^  ^     ^B 

l+Bjp^ 

It  is  useless  to  carry  this  table  further.  Enough  has  been 
done  to  show  the  error  of  exaggeration  of  ratio  into  which 
designers  have  fallen,  when  it  is  necessary  to  equalize  the 
power  of  cylinders  and  to  avoid  an  intermediate  drop  for 
the  sake  of  economy. 

Indeed,  in  all  engines^it  will  be  found  that  economy  of 
steam  as  well  as  smoothness  of  action  demands  that  no 
sudden  changes  of  pressure  shall  be  permitted,  and  there- 
fore it  will  be  found  advantageous  in  single  cylinder  engines 
where  clearance  cannot  be  indefinitely  reduced  to  use  enough 
compression  to  bring  the  back  pressure  up  to  the  initial 
pressure,  and  so  as  not  to  permit  an  explosion  in  the  cylinder 
at  the  beginning  of  each  stroke. 

The  less  the  clearance,  the  less  the  compression  required 
for  this  purpose,  and  consequently  the  less  the  power  of  the 
engine  is  absorbed  in  fulfilling  this  condition. 

(89.)  The  Influence  of  the  Receiver  and  Clear- 
ances.— If  the  receiver  be  considered,  it  is  obvious  that  the 
only  result  of  increasing  its  proportions  is  to  decrease  the 
mean  pressure  of  the  steam  against  both  pistons  up  to  the 
point  of  cut-off  e^  of  the  condensing  cylinder. 

This  will  decrease  the  power  of  the  condensing  cylinder 
and  increase  the  power  of  the  non-condensing  cylinder  up 
to  the  point  of  cut-off  e^. 

After  steam  is  cut  off  in  the  non-condensing  cylinder  the 
back  pressure  is  not  so  rapidly  raised  with  a  larger  receiver, 
which  results  in  a  further  increase  of  the  power  of  the  non- 
condensing  cylinder. 

After  steam  is  cut  off  in  the  condensing  cylinder,  its  power 


224  THE  RELATIVE  PROPORTIONS 

is  in  no  wise  affected  by  the  size  of  the  receiver,  as  the 
pressure  P^  =  ^—~  depends  on  the  initial  pressure,  the  ratio 

of  the  volumes  of  the  two  cylinders,  and  their  respective 
points  of  cut-off. 

This  pressure  P^  occurs  when  the  steam  is  just  being  cut 
off  from  the  condensing  cylinder ;  it  can  also  be  written 

P  — -jfJL 

'"Ee; 

We  observe  that  when  the  capacity  of  the  receiver  is 
assumed  very  great,  the  back  pressure  line  of  the  non-con- 
densing cylinder  comes  very  near  being  a  straight  line  ;  and 
further,  if  we  make  e,  equal  to  unity,  the  forward  pressure 
line  of  the  condensing  cylinder  comes  near  a  straight  line, 

and  P.  =  ^- 

XV 


The  ultimate  expansion  by  pressures  is 
E 


P.  _  Fo 


e,Pr    eVn 

That  is  to  say,  it  is  theoretically  quite  independent  of  the 
volume  of  the  receiver,  as  also  of  the  point  of  cut-off  in  the 
condensing  cylinder. 

If  we  fix  the  ultimate  expansion  E  of  the  steam  and  the 
point  of  cut-off  in  the  non-condensing  cylinder,  we  at  once 
determine  the  ratio  R  of  the  volumes  of  the  two  cylinders : 

'  n 

If  we  wish,  having  assumed  a  certain  ultimate  expansion 
E  and  ratio  of  volumes  of  cylinder  R,  to  determine  at  what 
point  the  condensing  cylinder  must  cut-off  in  order  to  ren- 
der the  work  for  the  steam  or  gas  a  maximum,  we  must 
so  arrange  that  the  terminal  pressure  ^P&  shall  equal  the 


OF  THE  STEAM-ENQINE.  225 

pressure  of  the  steam  in  the  receiver  at  the  moment  of  its 
admission :  this  would  require 

With  a  fixed  volume  of  receiver  we  have 

(.l+^)K.+  F,    _  .228) 

From  the  equation  for  the  compression  pressures  in  the 
non-condensing  cylinder  we  can  write  the  value  of  a;  =  the 
fraction  of  the  true  volume  at  which  its  exhaust-port  must 
be  closed,  so  that  the  pressure  in  the  receiver  shall  not  rise 
above  the  final  pressure  ePi. 

For  the  mean  absolute  back  pressure  while  the  non-con- 
densing piston  passes  from  e^  to  x  we  have 

(l-e,+k)V„+V.        ,      F+F„(l+^-0 

F.  •    ^  K+V.(_l+k-x) 

We  have  also  the  following  expression  for  the  absolute 

mean  back  pressure  on  the  non-condensing  piston  while 

compressing  from  x  to  k: 

ePi (1-X  +  k)  nat.  log  -. 
k 

That  is  to  say,  the  presence  of  a  receiver  is  always  pro- 
ductive of  a  loss  where  two  cylinders  are  worked  together, 
regardless  of  its  influence  on  the  cut-off  of  the  condensing 
cylinder,  and  it  is  entirely  unnecessary  when  cranks  are 
together  or  180  degrees  apart. 

Unfortunately,  we  cannot  suppress  the  clearances  alto- 
gether, and  therefore  from  the  above  we  have,  assuming 
K  =  0, 

'        Vn  +  BkX 


226 


THE  RELATIVE  PROPORTIONS 


OF  THE  STEAM-ENGINE.  "2,1*7 

Vr  will  represent  the  volume  of  the  connecting-pipes,  and 
require  its  use  in  actual  practice. 

Example. — Let  Pi  =  100  pounds  per  square  inch  (absolute). 
"  ^  =  8.    Then  R  =  2h    Let  -B  =  3  pounds 


"    Fc  =  8.    Then  Fn  =  3.20,  and  e  =  ;|. 

16 

"    K  =  l.     J.etk  =  k,  =  b  =  10%. 
-'°3.2o'-2KU.8)°W^'^-^^^-    See  equation  (228). 


Point  of  exhaust-closure  of 
non-condensing  cylinder 


I  a:  =  0.85. 


Power  of  non-condensing  cylinder  =  69.03  —  [12.49  +  6.75  -}-  7.16]  =  42.63.    (227  o) 
Power  of  condensing  cylinder  =2^  [12.49  +  6.66  —  2.7]  =  41.12.  (227  b) 

Had  there  been  no  back  pressure,  B,  and  no  clearances 
or  receiver,  the  cylinders  would  have  balanced.  Another 
approximation  will  be  sufficient,  provided  it  is  not  deemed 
that  losses  in  the  non-condensing  cylinder  and  passages  will 
reduce  its  power  sufficiently  when  steam  is  used. 

(90.)  The  Horse-Power  of  Compounded  Cylinders.^ 
— When  these  points  have  been  covered,  we  must  determine 
the  size  of  the  non-condensing  cylinder  for  the  required 
horse-power. 

If,  now,  we  assume  the  case  of  compounded  cylinders, 
with  cranks  together  or  180  degrees  apart,  no  receiver,  no 
drop  in  the  expansion,  no  cut-off  on  the  condensing  cylinder, 
and  no  clearances  or  compression,  we  have,  from  addition  of 
the  equations  for  the  work  of  the  two  cylinders  (227  «)  and 
(227  i), 

PF=  F„|eP.  Fl  +  natlog^l -iJS  I , 


228  THE  RELATIVE  PROPORTIONS 

or,  in  terms  of  the  volume  of  the  condensing  cylinder  and 

r» 

of  the  ultimate  expansion,  since  -^  =  e, 

PF=  Fc  1^^  [l  +  nat.  log  ^1 -^1 . 

That  is  to  say,  mathematically  it  can  be  shown  that,  the  same 
measure  of  expansion  being  used  in  both  cases,  the  power 
of  the  condensing  cylinder  alone  is  equal  to  the  combined 
powers  of  the  two  cylinders  of  a  compound  engine,  and  if 
we  neglect  initial  condensation  the  steam  economy  is  the 
same. 

The  mean  effective  pressure,  from  the  above  equation,  of 
the  condensing  cylinder  into  its  volume  gives  the  work  in 
one  stroke  =  FLA,  and  the  horse-power  is 

PLAN 


{HP)  = 


33000 


The  rest  of  the  proportioning  follows  from  what  has  here- 
tofore been  proved. 

(91.)  The  Influence  of  Cranks  at  Right  Angles.— 
Cranks  of  compound  engines  are  placed  at  angles  less  than 
180°,  for  convenience  of  handling  engines  which  have  no 
fly-wheel,  or  which  have  to  be  stopped  and.  started,  or  re- 
versed :  this  procedure  requires  the  presence  of  a  receiver 
or  compression  space,  and  converts  the  distances  of  the  pis- 
tons into  trigonometric  functions  relatively  to  each  other, 
but  in  no  wise  alters  the  principles  involved. 

When  compound  engines  must  be  frequently  started  or 
reversed,  it  is  important  that  they  be  so  arranged  as  to  avoid 
getting  on  their  centres ;  this  does  not  apply  to  pumping 
engines,  or  indeed  to  the  majority  of  stationary  engines,  but 
does  apply  with  a  great  deal  of  force  to  marine  engines. 

Some  designers  have  endeavored  to  obviate  this  difficulty 


OF  THE  STEAM-ENGINE.  229 

by  placing  the  cranks  160  degrees  apart,  thus  enabling  a 
very  small  dead  space  between  the  cylinders,  and  obviating 
trouble  with  the  engine  on  its  centre. 

This  case  differs  so  little  from  the  case  already  considered 
with  the  cranks  together  or  180  degrees  apart,  that  it  re- 
quires but  one  precaution  on  the  part  of  the  designer : 

The  non-condensing  cylinder  should  exhaust  before  the 
condensing  cylinder  takes  steam,  not  after,  as  that  would 
cause  a  sudden  rise  in  the  pressure  of  the  condensing  cylinder, 
with  the  attendant  loss. 

A  good  deal  of  weight  is  laid  on  equalizing  stresses  by 
placing  the  cranks  90  degrees  apart ;  but,  as  a  very  large 
number  of  engines  of  the  first  type  have  been  successfully 
designed,  there  is  no  reason  to  believe  it  impossible  in  the 
future  to  use  engines  with  cranks  180  degrees  apart. 

It  is  quite  possible  to  give  sufficiently  large  clearance- 
spaces  in  the  case  of  engines  with  cranks  at  right  angles  to 
fulfil  to  a  large  extent  the  functions  of  a  receiver,  but  it  is 
more  economical  to  reduce  the  clearances  of  the  steam- 
cylinders  as  much  as  possible  and  to  provide  a  receiver  of 
proper  size,  since  this  w^ill  avoid  sudden  changes  in  press- 
ure and  the  consequent  loss. 

In  what  follows  we  will  neglect  the  variation  of  the  pis- 
ton's positions  due  to  the  angular  position  of  the  connecting- 
rods. 

Assuming  the  engine  to  have  obtained  its  regular  move- 

eP 

ment,  we  will  have  P^  =  —  - . 
eJR 

The  sequence  of  exhaust  from  the  non-condensing  cylin- 
der, and  of  cut-off  of  the  condensing  cylinder,  renders  neces- 
sary the  presence  of  a  receiver  or  its  equivalent  when  cranks 
are  at  right  angles.  The  exhaust  from  the  non- condensing 
cylinder  occurs  just  as  the  piston  of  the  condensing  cylin- 
der reaches  mid-stroke,  and  so,  in  order  to  avoid  a  sudden 

20 


2S0  TITE  RELATIVE  PBOPORTIONS 

change  of  pressure  and  of  the  progress  of  expansion  in  the 
condensing  cylinder,  it  is  necessary  that  its  cut-off  be  earlier 
than  one-half  stroke. 

The  size  of  the  receiver  only  determines  the  fluctuation  of 
the  pressures  in  it.  The  smaller  the  receiver  the  greater 
the  fluctuations. 

It  is  obvious  from  what  has  already  been  shown  that  at 
the  instant  of  cut-ofl*  of  the  condensing  cylinder  the  pressure 
in  it  and  also  in  the  receiver,  as  well  as  the  back  pressure 
in  the  non-condensing  cylinder,  equals  P^. 

At  the  instant  of  reaching  the  end  of  the  stroke  of  the 
non-condensing  cylinder  it  voids  into  the  receiver  its  steam 
at  a  pressure  eP,,. 

If  we  wish  this  event  to  occur  with  as  little  disturbance 
as  possible,  we  must  make  the  pressure  at  that  event  equal 
in  non-condensing  cylinder  and  receiver. 

The  cranks  being  at  right  angles  have  certain  definite 
positions  with  regard  to  each  other  at  all  times,  and  the 
position  of  one  piston  being  fixed,  that  of  the  other  can  be 
deduced.     If  now  we  assume  the  cut-ofi"  e^  of  the  condensing 

cylinder  to  be  — ^,  it  will  be  coincident  with  the  exhaust  of 

the  non-condensing  cylinder,  and  the  equation 

eP, 


Pr 


e,R 


becomes  e^  =  — ;  that  is,  R  =  2,  very  nearly,  for  ej^  =  h 
R 

As  the  condensing  cylinder  completes  its  stroke  under  the 
pressure  of  expanded  steam  not  connected  with  the  receiver, 
its  ratio  can  be  somewhat  greater,  and  consequently  the 
ultimate  expansions  greater,  without  departing  from  the 
condition  of  equalized  cylinder  power. 

The  exit  from  the  receiver  to  the  condensing  cylinder 


OF  Tim  STEAM-ENGINE.  231 

being  closed,  the  piston  of  the  non-condensing  cylinder  now 
presses  back  the  steam  in  that  cylinder  and  the  receiver 
until  it  has  reached  half-stroke ;  when  the  pressure  is  a 
maximum  P^,  we  can  write  the  following  equation : 


epJv^+v\  =  P„{^V^+V, 


In  this  equation  we  can  fix  P„  and  determine  Vr,  or  vice 
versa. 

In  general  we  can  say  that  e^  must  be  somewhat  greater 

than  —  in  order  to  receive  the  exhaust  steam  from  the  non- 

condensing  cylinder  without  forcing  it  back. 

If  we  assume  that  the  terminal  pressure  of  the  non-con- 
densing cylinder  must  equal  that  in  the  receiver  at  the 
moment  of  opening  communication,  we  can  write  the  fol- 
Fig.  42. 


lowing  equation,  in  which  x  =  the  distance  of  the  non-con- 
densing piston : 

PAxVr.+  Vrl=eP,(kVn+Vr) 
l^J^ 

X  =  -— i/cj  (mj~~  gj^  -  k. 

We  have  then 

!+;{;  

e^Rk  -  -----  +  i/^i  (T +^)  -  ^i'^ 


232  THE  RELATIVE  PROPORTIONS 

At  the  instant  of  cut-off  a  quantity  of  steam  is  left  in  the 
receiver  and  non-condensing  cylinder  at  a  pressure  P^.  As 
the  cut-off  e^  is  assumed  earlier  than  half-stroke,  we  can 
then  write  the  following  equation : 

The  two  indeterminate  quantities  in  this  equation  are  P„ 
and  Vr,  either  of  which  can  be  fixed  and  the  other  deduced. 
It  will  be  observed  that  the  clearance  of  the  condensing 
cylinder  is  included,  and  therefore  that  P^  is  the  pressure  at 
the  instant  the  piston  of  the  condensing  cylinder  is  at  the 
end  of  the  stroke,  its  valve  being  assumed  to  have  lead  and 
a  perfect  vacuum  to  be  obtained. 

It  will  be  observed  that  the  presence  of  a  receiver  has 
the  effect  of  reducing  the  power  of  the  non-condensing  cyl- 
inder when  P^  is  greater  than  ePj,  as  it  always  should  be. 
The  greater  the  size  of  the  receiver  the  less  the  increase  of 
Prn ;  but  this  increase  of  P^  being  made  gradually,  and  the 
power  taken  from  the  non-condensing  cylinder  being  restored 
to  the  condensing  cylinder  by  reason  of  the  increased  press- 
ure before  cut-off"  occurs,  it  would  not  seem  detrimental  to 
economy  to  make  receivers  as  small  as  possible. 

The  disadvantage  of  these  high  back  pressures  at  mid- 
stroke  in  the  non-condensing  cylinder  arises  from  the  dim- 
inution of  its  power. 

The  only  result  of  using  a  very  large  receiver,  when  cut- 
ting off"  steam  in  the  condensing  cylinder  earlier  than  the 

point  — ,  is  to  prevent  the  pressure  in  the  receiver  from 
P 

rising  much  higher  than  the  terminal  pressure  of  the  non- 
condensing  cylinder. 

A  high  back  pressure  at  mid-stroke  of  the  non-con- 
densing cylinder  also  means  a  high  initial  pressure  of  the 


OF  THE  STEAM-ENGINE.  233 

condensing  cylinder,  and,  consequently,  increased  power  in 
the  condensing  cylinder. 

That  is,  a  large  receiver  operates  to  prevent  disproportion 
in  the  power  of  two  cylinders  when  proportioned  according 
to  the  criterion  given  in  the  preceding  pages  of  this  chapter, 

requiring  also  that  the  point  Cj  =  — -  very  nearly,  but  will 

be  found  not  to  be  so  economical  of  steam  as  a  very  small 
receiver,  or  none  at  all. 

The  clearances  necessarily  are  regarded  as  receiver-space. 

To  sum  up  the  discussion  : 

With  cranks  at  right  angles,  we  cannot  cut-off  later  than 
one-half  stroke  in  the  condensing  cylinder  without  a  double 
admission  to  it,  and  consequent  loss. 

We  cannot  cut-off  earlier  than  —  without  pressing  the 

XV 

steam  from  the  receiver  back  into  the  non-condensing  cylin- 
der, because  the  steam  wall  rise  to  a  higher  pressure  in  the 
receiver  than  the  terminal  pressure  in  the  non-condensing 
cylinder.  If  this  is  done  only  to  a  small  extent  it  may  not 
prove  a  serious  evil. 

If  we  use  a  receiver  of  any  considerable  size,  we  must 
submit  to  a  drop  from  the  terminal  pressure  of  the  non- 
condensing  cylinder  to  the  pressure  in  the  receiver,  with 

the  consequent  loss,  or  make  e^  =  —  very  nearly. 

XI 

If  we  do  not  use  any  receiver,  or  use  only  a  very  small 
one,  we  can  effect  a  greater  economy  of  steam ;  but  the  power 
of  the  two  cylinders  cannot  be  equalized  without  pushing  the 
ultimate  expansion  beyond  all  reasonable  limits  and  dimin- 
ishing the  concentration  of  pow'er  so  essential  to  all  steam- 
engines,  unless  we  make  the  point  of  cut-off  of  the  con- 
densing cylinder  later  than  2  stroke,  and  thus  submit  to  a 
double  admission  or  increase  of  pressure  during  expansion. 


234  THE  RELATIVE  PROPORTIONS 

(92.)  Condensation  in  Compounded  Cylinders.— It 

has  been  with  the  greatest  difficulty  that  the  writer  has  found 
data  from  engines  proved  steam-tight. 

Indeed,  it  is  safe  to  say  that  nearly  every  engine  leaks 
badly,  unless  unusual  precautions  have  been  taken  in  fitting 
and  direct  experimental  proof  is  given  to  the  contrary. 

The  diagram  of  the  example  already  solved  will  enable 
us  to  follow  clearly  the  steam-pressures  and  temperatures  in 
the  compounded  cylinders. 

The  steam  enters  the  non-condensing  cylinder  at  a  pressure 
of  100  pounds  (^6  =  327.5),  and  is  condensed  upon  walls  hav- 
ing a  temperature  not  lower  than  2302°,  corresponding  to  a 
receiver  pressure  of  21.3  pounds.  This  condensation  can  be 
still  further  reduced  by  compression  in  the  non-condensing 
cylinder,  as  shown. 

AVhen  the  steam  has  once  been  cut  off  in  the  non- 
condensing  cylinder,  all  further  demands  upon  the  boiler 
cease  for  that  stroke.  The  cylinders  and  receiver  must 
satisfy  their  demands  for  condensation  from  what  is  in  them 
already. 

The  final  condensation  in  the  condensing  cylinder  just 
before  opening  to  exhaust  is  proportional  to  204°  (12i 
pounds)  minus  141.6°  (3  pounds),  and  is  thrown  away 
through  the  exhaust,  without  appearing  on  the  diagram. 

Had  a  single  cylinder  been  used  of  the  same  size  as  the 
condensing  cylinder,  the  final  condensation  loss  would  prove 
the  same ;  but  the  initial  condensation  for  the  same  number 
of  expansions  and  work  would  have  been  much  greater,  thus 
causing  a  larger  volume  of  vaporous  steam  to  disappear 
before  expansion  begins,  and  lessening  the  work  {PV)  done 
by  a  given  weight  of  steam. 

This  is  the  explanation  of  the  greater  efficiency  of  com- 
pounded cylinders. 

For  any  given  conditions  the  comparison  between  single 


OF  THE  STEAM-ENQINK 


235 


236  TEE  RELATIVE  PROPORTIONS 

and  compounded  cylinders  is  made  by  means  of  formula 
(220  6)  and  analogous  ones. 

It  is  in  improved  methods  of  study  and  experiment  that 
we  must  hope  for  advancement,  rather  than  in  the  piling  up 
of  chaotic  masses  of  more  or  less  accurate,  and  almost  al- 
ways incomplete,  experimental  work,  valuable  only  for  com- 
mercial purposes.  One  series  of  experiments  on  a  compound 
engine,  carried  out  with  care  and  skill,  will  give  us  a  better 
basis  than  we  have  as  yet  for  comparison  with  theoretical 
results,  which  we  must  use  to  guide  us,  knowing  them  not 
to  be  precise,  but  feeling  them  far  more  accurate  than  at- 
tempted generalizations  from  data  which  are  in  no  wise 
comparable. 

(93.)  Methods  of  Experimentation.— In  order  to  facil- 
itate the  great  labor  of  arranging  experiments  upon  boilers 
and  steam-engines,  the  writer  appends  two  codes,  drawn  up 
by  him  at  the  request  of  the  Franklin  Institute.  These 
codes  were  adopted  and  used  by  the  Institute  during  its 
International  Electrical  Exhibition  of  1884,  at  Philadelphia. 

(94.)  Code  of  the  Proposed  Quantitative  Tests  for 
the  Evaporative  Efficiency  of  Boilers  at  the  Inter- 
national Electrical  Exhibition,  by  the  Franklin 
Institute,  1884. 

SPECIAL  NOTICE. 

Boilers  may  be  exhibited  and  used  at  the  International 
Electrical  Exhibition,  but  will  not  have  quantitative  tests 
made  of  their  efficiency  unless  formal  application  is  made 
and  the  subjoined  code  accepted  before  July  15,  1884. 

Competitive  tests  will  not  be  made  unless  at  the  joint  re- 
quest of  the  parties  desiring  a  competitive  test,  and  after 
they  have  agreed  to  and  subscribed  to  this  code  and  fixed 
upon  a  rating  for  the  points  enumerated  in  Article  4. 


OF  THE  STEAM-ENGINK  237 

The  Committee  of  Judges  reserve  the  right  to  limit  the 
number  of  tests  made,  should  time  and  opportunity  not 
permit  all  the  tests  desired  to  be  completed. 

Section  I. — Preliminaries  to  the  Tests. 

Article  1.  Capacity. — The  boilers  entered  may  be  of 
any  capacity  having  an  evaporative  power  not  less  than 
seven  hundred  and  fifty  pounds  of  water  per  hour. 

Each  boiler  must  be  so  drilled  as  to  enable  its  whole 
internal  capacity  to  be  determined  by  being  completely 
filled  and  emptied  of  water.  Proper  cocks,  piping,  etc., 
must  be  so  placed  as  to  enable  this  to  be  done  readily. 

Art.  2.  Pipes  and  Valves. — Each  exhibitor  will  furnish  all 
the  pipes  and  valves  necessary  to  make  connection  with  the 
main  water-  and  steam-pipes  in  a  proper  manner,  and  subject 
to  the  orders  of  the  superintendent.  He  will  also  make  any 
alterations  in  water-  and  steam-pipes  required  for  the  tests, 
furnishing  all  tools,  piping,  cocks,  and  mechanical  labor  at 
his  own  cost. 

Art.  3.  Space. — Each  exhibitor  will  be  furnished  with 
space  at  the  regular  rates  established  for  the  Exhibition,  in 
which  space  he  must  build  his  foundations  and  boiler-setting, 
and  make  connection  with  the  chimney-flue,  if  required,  at 
his  own  cost,  and  subject  to  the  approval  of  the  superin- 
tendent. 

Art.  4.  Specifications. — Each  exhibitor  must  furnish  to 
the  Chairman  of  the  Committee  of  Judges  on  Steam-boilers 
such  description  and  drawing,  both  of  the  boiler  in  position 
and  of  the  details  of  the  boiler,  as  will  facilitate  the  labor 
of  that  Committee,  together  with  his  claims  as  to  meritorious 
points  for  his  exhibit. 

The  following  points  will,  have  special  consideration  \ 

1.  Economy  of  fuel. 

2.  Economy  of  material  and  labor  of  construction. 


238  THE  RELATIVE  PROPORTIONS 

3.  Evaporative  power.     (Space  occupied.) 

4.  Simplicity  and  accessibility  of  parts. 

5.  Durability  of  whole  structure. 

Exhibitors  desiring  a  competitive  test  made  must  agree 
upon  a  rating  for  these  points  before  it  will  be  made. 

Exhibitors  must  also  file  the  following  data : 

Area  of  heating  surface  to  the  nearest  hundredth  of  a 
foot. 

Area  of  grate  surface  to  the  nearest  hundredth  of  a  foot. 

Area  of  calorimeter  to  the  nearest  hundredth  of  a  foot. 

Area  of  chimney-flue  to  the  nearest  hundredth  of  a  foot. 

Height  of  chimney  required. 

Number  of  pounds  of  coal  per  square  foot  of  grate  to  be 
burned  per  hour. 

Should  the  calculations  of  the  Committee  of  Judges  differ 
in  result  from  those  of  the  exhibitor,  he  will  be  required  to 
give  all  the  details  of  his  calculations,  and  an  agreement 
must  be  reached  before  proceeding  with  the  test. 

Section  II. — Preparations  for  the  Tests. 

Art.  5.  Coal. — Anthracite  coal  will  be  used,  and  will  be 
furnished  free  of  charge,  provided  the  steam  made  is  used 
for  the  general  purposes  of  the  Exhibition. 

The  same  quality  and  size  of  coal  will  be  used  in  all  the 
tests,  unless  special  arrangements  be  made  for  another  kind 
of  fuel* 

An  analysis  will  be  made  of  the  coal  used.  The  coal  will 
be  weighed  to  the  boiler. 

Art.  6.  Water. — The  water  used  will  be  taken  from  the 
city  mains.  The  feed-water  for  the  boilers  will  be  weighed 
by  means  of  scales  and  a  large  tank,  and  will  be  run  into  a 
smaller  supplemental  tank,  from  which  it  will  be  pumped 
into  the  boiler  by  means  of  a  feed-pump  actuated  by  steam 
from  the  boilers. 


OF  THE  STEAM-ENQINE.  239 

The  temperature  of  the  feed- water  will  be  taken  by  means 
of  a  standard  thermometer,  in  the  supplemental  tank. 

Art.  7.  Pressure. — The  steam-pressure  used  shall  not  ex- 
ceed ninety  pounds  per  square  inch  by  the  gauge,  unless  by 
special  arrangement  with  the  Committee  of  Judges. 

A  standard  gauge  will  be  used,  and  also  a  standard  ther- 
mometer immersed  jn  a  mercury  pocket  in  the  steam-space. 

Art.  8.  Safety-Valve. — The  safety-valve  will  be  set  to 
blow  off  at  ten  pounds  above  the  pressure  fixed  upon. 

Art.  9.  Leaks.-^Wiih'm  twenty-four  hours  preceding  the 
test  of  a  boiler,  it  must  be  subjected  to  hydraulic  pressure 
ten  pounds  greater  than  its  steam -pressure  during  the  test, 
and  proved  to  be  perfectly  tight. 

Art.  10.  Atlendants. — The  attendants  in  charge  of  the 
boiler  tested  must  be  approved  by  the  party  whose  boiler  is 
tested  and  by  the  Judges.  All  attendants  are  to  be  subject 
to  the  ©rders  of  the  Judges  during  the  progress  of  the  test. 

Art.  11.  Ashes. — All  ashes  will  be  weighed  on  being 
withdrawn  from  the  ash-pit,  and  must  not  be  damped  until 
w^eighed. 

Art.  12.  Calorimeters. — The  calorimeters  used  will  con- 
sist of  a  barrel,  scale,  and  hand  thermometer.  Two  calo- 
rimeters will  be  used,  and  simultaneous  observations  made 
at  fifteen-minute  intervals. 

Art.  13.  Fires. — The  exhibitor  shall  be  allowed  one  day 
previous  to  the  test  to  clean  boilers  and  grates. 

The  steam  having  reached  the  required  pressure,  the  ash- 
pit shall  be  thoroughly  cleaned  and  swept,  and  thereafter 
the  fire  maintained  as  nearly  uniform  as  possible,  the  test 
closing  with  the  same  depth  and  intensity  of  fire  as  it  opened. 

This  point  is  to  be  decided  by  the  Judges,  who  may  make 
allowance  if  it  be  clearly  shown  to  have  been  impossible  to 
maintain  uniform  fires. 

If  in  the  judgment  of  the  Committee  of  Judges  the  firing 


240  THE  RELATIVE  PROPORTIONS 

is  inefficiently  or  improperly  done,  the  test  may  be  terminated 
at  any  time,  and  a  repetition  of  the  test  refused. 

Art.  14.  Pyrometer. — The  temperature  of  the  gases  of 
combustion  immediately  upon  entering  the  chimney-flue 
shall  be  taken  by  means  of  a  suitable  pyrometer,  read  at 
fifteen-minute  intervals,  and  close  to  the  boiler. 

ApvT.  15.  Manometer  and  Barometer. — The  vacuum  in  the 
chimney-flue  shall  be  taken  by  means  of  a  water  manometer, 
read  at  fifteen-minute  intervals.  A  barometer  will  be  read 
simultaneously. 

Art.  16.  Duration. — Unless  otherwise  arranged,  the  tests 
will  last  ten  hours. 

Art.  17.  Economy  and  Efficiency  of  the  Boiler. — The  level 
of  the  water  in  the  boiler  and  the  state  of  the  fire  must  be 
kept  as  nearly  constant  as  possible  during  the  whole  of  the 
trial. 

The  weight  of  the  water  in  the  boiler  for  each  one-quarter 
of  an  inch,  on  the  glass  water-gauge,  will  be  carefully  deter- 
mined and  recorded  previous  to  the  test,  and  proper  correc- 
tion for  unavoidable  changes  of  level  made. 

The  weight  of  water  fed  to  the  boiler,  subject  to  proper 
corrections,  will  be  multiplied  by  its  observed  thermal  value 
as  steam.  From  this  product  the  thermal  units  of  heat 
brought  in  by  the  feed  will  be  subtracted. 

The  remainder  will  be  divided  by  nine  hundred  and  sixty- 
six  and  seven-hundredths  British  thermal  units,  giving  the 
number  of  pounds  of  water  evaporated  from  and  at  212° 
Fahrenheit. 

This  latter  quantity  will  be  divided  by  the  weight  of  coal 
burned,  less  weight  of  dry  ashes,  giving  the  number  of 
pounds  of  water  evaporated  per  pound  of  combustible. 
This  shall  be  taken  as  the  measure  of  the  efficiency  of  the 
boiler. 

The  nominal  horse-power  of  the  boiler  will  be  deduced 


OF  THE  STEAM-ENGINE.  241 

by  dividing  the  number  of  pounds  of  water  evaporated  from 
and  at  212°  Fahrenheit  per  hour  by  thirty. 

The  evaporative  power  of  the  boiler  will  be  determined 
by  dividing  the  nominal  horse-power  of  the  boiler  by  the 
number  of  cubic  feet  of  space  it  occupies. 

The  space  occupied  by  a  boiler  and  its  appurtenances  will 
be  regarded  as  the  product  of  the  square  feet  of  floor- space 
occupied  by  its  extreme  height  in  feet. 

(95.)  Code  of  the  Quantitative  Tests  proposed  for 
the  Steam-Engines  at  the  International  Electrical 
Exhibition,  1884,  of  the  Franklin  Institute,  of  the 
State  of  Pennsylvania. 

SPECIAL  NOTICE. 

Parties  exhibiting  engines,  who  may  desire  quantitative 
tests  made  of  them,  must  make  formal  application  for  such 
tests  before  July  15,  1884. 

Engines  can  be  exhibited,  but  will  not  be  tested  unless 
formal  application  and  agreement  to  the  code  are  completed 
within  the  specified  time. 

Parties  desiring  to  have  tests  made  of  their  engines  can 
have  them  made  by  so  signifying  and  by  subscribing  to  and 
fulfilling  the  conditions  of  the  code. 

All  tests  will  be  quantitative,  and  will  not  be  abridged, 
save  by  special  agreement  with  the  Judges. 

Tests  of  regularity  of  speed  will,  however,  be  made  inde- 
pendently of  other  measurements. 

The  Committee  reserves  the  right  to  limit  the  number  of 
engines  tested,  and  to  elect  which  engines  shall  be  tested,  if 
time  will  not  permit  complete  tests  of  all. 

Competitive  tests  will  not  be  made  save  on  the  joint  ap- 
plication of  the  two  or  more  parties  desiring  them,  who 
must  agree  on  the  rating  of  the  various  points  of  the  en- 

21 


242  THE  RELATIVE  PROPORTIONS 

gines  (see  Article  9)  previous  to  the  tests,  and  subscribe  in 
the  code,  agreeing  to  abide  by  the  decision  of  the  Judges 
without  appeal. 

Section  I. — Conditions  op  Exhibition  and  Test. 

Article  1.  Cylinders. — The  cylinders  of  the  engines  en- 
tered may  be  of  any  capacity  and  proportion  of  stroke  to 
diameter. 

Art.  2.  Indicator  Connections. — Each  cylinder  shall  be 
drilled  and  tapped  by  the  builder  for  indicator  connections, 
by  means  of  one-half  inch  pipe,  in  the  usual  manner,  and 
to  the  satisfaction  of  the  Judges.  Pet  drainage-cocks  must 
be  on  the  cylinder.  The  cross-head  or  other  moving  part 
must  be  drilled  for  the  indicator  cord  attachment. 

Art.  3.  Clearance. — Each  cylinder  shall  be  drilled  and 
plugged  at  both  ends,  so  as  to  admit  of  being  completely 
filled  with  water  and  emptied  by  means  of  a  one-half  inch 
pipe,  in  order  to  determine  the  clearance  and  the  piston  dis- 
placement of  one  stroke  at  each  end.  These  data  will  be 
obtained  both  hot  and  cold. 

Art.  4.  Valves. — The  steam-  and  exhaust- valves  will  be 
tested  under  full  steam-pressure,  ninety  (90)  pounds  per 
square  inch  by  the  gauge,  unless  some  other  pressure  has 
been  agreed  upon  for  the  test. 

Art.  5.  Piston  Packing.  —  The  tightness  of  the  piston 
packing  will  be  determined  by  removing  the  back  cylinder- 
heads  and  subjecting  the  piston  to  full  boiler  pressure  on 
each  centre. 

Art.  6.  Fly -Wheel. — Each  maker  is  requested  to  use 
such  diameter  of  band  fly-wheel,  or  of  pulley,  as  shall  give 
a  belt  speed  of  4000  feet  per  minute. 

Should  he  require  a  difierent  belt  speed,  he  will  specially 
note  the  same  in  communicating  with  the  Exhibition  Com- 
mittee. 


OF  THE  STEAM-ENGINE.  243 

Art.  7.  Steam-Pipes. —  Each  exhibitor  will  be  required 
to  fiirnish  his  own  connection  with  the  main  steam-pipe,  the 
main  injection-pipe,  and  the- main  overflow-pipe  or  tanks. 

Art.  8.  Space. — Each  exhibitor  will  be  furnished  with 
space  at  the  regular  rates  established  for  the  Exhibition,  in 
which  space  he  must  build  his  foundations  at  his  own  cost, 
and  subject  to  the  approval  of  the  superintendent. 

Art.  9.  Specifications. — Each  exhibitor  will  communicate 
to  the  Chairman  of  the  Committee  of  Judges  on  Steam- 
Engines  such  description  and  drawings  of  the  engine  ex- 
hibited as  will  facilitate  the  labors  of  that  Committee, 
together  with  his  claims  as  to  the  meritorious  points  for  his 
exhibit. 

The  following  points  will  have  special  consideration : 

1.  Economy  of  steam. 

2.  Kegularity  of  speed. 

3.  Concentration  of  power. 

4.  Durability  of  construction. 

5.  Simplicity  of  design. 

6.  Excellence  of  proportions. 

7.  Finish  of  parts. 

Each  exhibitor  must  file  the  following  data : 

Diameter  of  the  steam-cylinder  to  the  nearest  hundredth 
of  an  inch. 

Diameter  of  the  piston-rod  to  the  nearest  hundredth  of 
an  inch. 

Diameter  of  the  steam-pipe  to  the  nearest  hundredth  of 
an  inch. 

Diameter  of  the  exhaust-pipe  to  the  nearest  hundredth  of 
an  inch. 

Diameter  of  the  band,  or  fly-wheel,  to  the  nearest  hun- 
dredth of  an  inch. 

Width  of  the  face,  or  fly-wheel,  to  the  nearest  hundredth 
of  an  inch. 


244  THE  RELATIVE  PROPORTIONS 

Weight  of  the  fly-wheel  in  pounds. 

Area  of  the  steam-ports  each  to  the  nearest  hundredth  of 
an  inch. 

Area  of  the  exhaust-ports  each  to  the  nearest  hundredth 
of  an  inch. 

Stroke  of  the  engine  to  the  nearest  hundredth  of  an  inch. 

Indicated  horse-power  of  the  engine  w^hen  working  most 
economically. 

Revolutions  of  the  crank  per  minute. 

Weight  of  the  whole  engine,  exclusive  only  of  the  fly- 
wheel. 

If  a  condenser  is  used  and  driven  by  the  engine. 

Diameter  of  the  air-pumps  to  the  nearest  hundredth  of 
an  inch. 

Diameter  of  the  injection-pipe  to  the  nearest  hundredth 
of  an  inch. 

Diameter  of  the  overflow-pipe  to  the  nearest  hundredth 
of  an  inch. 

Stroke  of  the  air-pump  piston  to  the  nearest  hundredth 
of  an  inch. 

If  an  independent  condenser  is  used  that  is  not  driven  by 
the  engine. 

Diameter  of  the  injection-pipe  to  the  nearest  hundredth 
of  an  inch. 

Diameter  of  the  overflow-pipe  to  the  nearest  hundredth 
of  an  inch. 

Drawings  of  the  condenser  used,  any  other  data  peculiar 
to  it,  and  a  full  description  of  it. 

Section  II. — Peeparations  for  the  Test. 

Art.  10.  Steam. — The  steam  for  the  tests  will  be  furnished 

by  the  Exhibition  boilers,  and  will  come  from  boilers  specially 

set  apart  for  the  purpose  of  the  tests.     It  will  be  charged 

for  at  regular  rate  of  three  (3)  cents  per  indicated  horse 


OF  THE  STEAM-ENGINE.  245 

power  per  hour.  Steam,  if  desired,  will  be  fiirnished  to 
exhibitors  one  week  before  the  tests  are  made. 

No  charge  will  be  made  for  the  services  of  attendants  or 
experts,  or  the  use  of  apparatus,  unless  in  some  extraordi- 
nary case,  when  the  cost  will  be  fixed  by  the  superintendent 
of  the  Exhibition.  No  charge  against  the  engine  will  be 
made  for  steam  when  its  power  is  ordered  by  the  superin- 
tendent for  the  other  purposes  of  the  Exhibition. 

Art.  11.  Pressure. — The  steam-pressure  used  will  be  sub- 
ject to  the  wish  of  the  exhibitor,  but  shall  not  exceed  ninety 
(90)  pounds  per  square  inch,  by  the  gauge. 

A  special  standard  gauge  will  be  used  during  the  test, 
and  subjected  to  careful  tests  before  and  after  use. 

Art.  12.  Safety -Valve. — The  safety-valve  will  be  set 
to  blow  off  at  ten  (10)  pounds  above  the  pressure  fixed 
upon. 

Art.  13.  Quality  of  the  Steam. — The  thermal  value,  the 
temperature,  and  the  pressure  will  be  taken  by  means  of 
scale  calorimeters,  thermometers,  and  standard  gauges  at 
the  boiler,  at  the  steam-chest,  and  at  the  exhaust,  if  the 
engine  is  non- condensing. 

The  thermometers,  calorimeters,  etc.,  will  be  furnished  by 
the  Exhibition,  but  the  exhibitor  must  do  such  mechanical 
work,  must  furnish  such  piping,  tools,  and  materials  as  are 
necessary  to  make  the  required  attachments,  at  his  own  cost, 
and  subject  to  the  orders  of  the  Committee  of  Judges. 

Art.  14.  Temperature. — The  temperatures  of  injections 
and  of  hot-well  will  be  taken  with  standard  thermometers 
in  the  case  of  condensing  engines. 

Art.  15.  Water. — The  water  used  will  be  taken  from  the 
city  mains. 

The  feed-water  for  the  boilers  will  be  weighed  by  means 
of  scales  and  a  large  tank,  and  will  be  run  into  a  smaller 
supplemental  tank,  from  which  it  will  be  pumped  into  the 


246  THE  RELATIVE  PROPORTIONS 

test  boilers  by  means  of  a  feed-pump,  actuated  by  steam 
from  other  boilers. 

The  condensing  water  used  will,  in  the  case  of  condensing 
engines,  be  measured  after  leaving  the  hot- well  in  two  care- 
fully-gauged tanks,  alternately  filled  and  emptied,  the  tem- 
perature also  being  taken. 

The  known  weight  of  steam  used  will  be  subtracted  from 
the  overflow. 

The  injection  water  will  be  weighed  in  large  tanks,  and 
its  temperature  taken. 

The  injection  water  will  not  be  delivered  under  pressure. 

Art.  16.  Speed  of  Engine. — The  number  of  revolutions 
of  the  engine  will  be  taken  by  a  continuous  counter  attached 
to  the  crank-shaft. 

The  variations  in  speed  for  one  minute  will  be  taken  at 
each  quarter  of  an  hour  by  means  of  an  electric  chronograph 
connected  with  a  standard  clock  beating  seconds. 

The  variations  in  speed  during  one  stroke  will  be  taken 
by  an  acoustic  chronograph  at  fifteen-minute  intervals. 

Special  tests  of  speed  alone,  under  varying  loads,  will  be 
made  if  desired,  and  close  attention  will  be  had  to  this  point 
in  all  cases. 

Art.  17.  Barometric  Measurements. — A  standard  barom- 
eter and  thermometer  will  be  read  at  fifteen-minute  intervals 
during  the  trial. 

Art.  18.  Vacuum. — The  vacuum  of  condensing  engines 
will  be  read  by  a  gauge,  carefully  compared  before  and  after 
the  trials. 

Art.  19.  Testing  of  Gauges,  Indicators,  etc. — All  of  the 
gauges,  indicators,  and  thermometers  used  shall  be  carefully 
tested  before  and  after  the  trials,  and  the  party  whose  en- 
gine is  tested  shall  have  the  right  to  be  present  in  person  or 
by  agent  at  these  tests. 

Art.  20.   Diagrams. — The  indicator  diagrams   will  be 


OF  THE  STEAM-ENGINE.  247 

taken  at  fifteen-  (15)  minute  intervals,  and  will  be  read  for 
initial  pressure,  pressure  at  cut-off,  terminal  pressure,  coun- 
ter-pressure at  mid-stroke,  maximum  compression  pressure, 
mean  effective  pressure,  point  of  cut-off,  release  of  steam, 
exhaust-closure. 

From  the  diagrams  will  be  computed  the  indicated  steam 
at  the  point  of  cut-off  and  at  release,  as  also  the  actual  steam 
from  boilers  per  horse-power  per  hour. 

Art.  21.  Load  of  the  Engine. — The  Committee  of  Judges 
will  test  the  engine  at  the  load  desired  by  the  exhibitor  of 
it,  unless  circumstances  shall  render  it  impossible  to  meet 
his  wishes. 

K  the  load  does  not  exceed  seventy-five  (75)  indicated 
horse-power,  the  net  load  will  be  measured  by  a  trans- 
mitting dynamometer. 

Art.  22.  Friction  Diagrams. — At  the  close  of  the  regular 
trial,  the  engine  will  have  its  belt  taken  off,  and  be  run  for 
one  hour  for  friction  diagrams. 

Art.  23.  Duration  of  the  Trials. — Unless  otherwise  ar- 
ranged, the  trials  will  last  ten  (10)  hours. 

Art.  24.  Economy  and  Efficiency  of  the  Engine. — No  ac- 
count will  be  taken  of  the  coal  burned ;  but  the  economy 
of  the  engine  will  be  deduced  from  the  actual  steam  used 
and  water  weighed  to  the  boiler. 

The  trial  will  begin  with  the  established  pressure. 

The  level  of  the  water  in  the  boiler,  and  the  pressure  of 
the  steam,  will  be  kept  as  nearly  constant  as  possible  during 
the  whole  of  the  trial. 

The  whole  weight  of  the  water  fed  to  the  boiler,  subject 
to  proper  deductions  for  waste,  and  to  corrections  for  varia- 
tion of  level  in  the  boiler,  will  be  multiplied  by  its  thermal 
value  as  steam  at  the  steam-chest,  and  divided  by  the 
product  of  the  indicated  horse-power  of  the  engine,  and 
the  number  of  hours  of  the  test. 


248        PROPORTIONS  OF  THE  STEAM-ENGINE. 

The  resulting  quotient  will  be  used  to  divide  twenty-five 
hundred  and  fifty-seven  and  sixty-nine  one-hundredths 
(2557.69)  British  thermal  units,  giving  the  efiiciency  of  the 
engine  as  compared  with  the  mechanical  equivalent  of  the 
heat  furnished  to  it,  and  therefore  its  efficiency  as  a  means 
of  converting  heat  into  work. 

The  net  horse-power  of  the  engine  will  be  used  for  com- 
putation similarly  to  the  indicated  'horse-power,  and  the 
result  will  be  taken  as  the  measure  of  the  efficiency  of  the 
engine,  both  as  a  means  of  converting  heat  into  work  and 
as  a  machine  for  the  transmission  of  power. 

This  latter  shall  be  considered  the  true  measure  of  the 
efficiency  of  the  engine. 


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